Below is the pdf for the random variable X: 2- (4) (₂5₂) (²) 9 0, f(x) = x = 0, 1, 2 otherwise Find F(1.5). If needed, round to FOUR donim
Q: A random variable X follows a gamma distribution having a mean of 384 and a CoV of 0.316. What is…
A: Given information: Given that the random variable X follows a gamma distribution with a mean of 384…
Q: Let X be a random variable with mean E[X] = 20 and variance Var(X)= 3. Define Y = 3 - 6X. Calculate…
A: We have given that, Let X be a random variable with mean E[X] = 20 and variance Var[X] = 3 We know…
Q: A random variable Y has a uniform distribution over the interval (?1, ?2). Derive the variance of Y.…
A:
Q: Suppose the random variable X has pdf Exp(- (u - 2)²), fx(u) = K 2√2π 0≤u≤ 4, otherwise. where K is…
A:
Q: Let Xi, X2, f(x;e)- ee *I c0.00 (x). Find a l00y or percent confidence interval for the the…
A:
Q: For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|Y ))
A: Given, Two random variables X and Y such that X~Exp(0.5) and Y|X=x ~N(5,x2)
Q: Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y…
A:
Q: A coin which has probability 0.88 of coming up Heads is tossed three times. Let Y be the number of…
A: It is given that probability of getting head is 0.88 and coin is tossed three times.
Q: 2. Let X be a random variable with E[X] = 15 and Var[X] = 10. Suppose Y = 2X – 7, Use the properties…
A: Given,E(X)=15Var(X)=10and Y=2X-7
Q: E and F are independent variables with variances of 7 and 9, respectively. Given this, Var(2E - F +…
A:
Q: U is a uniform (0, 1) random variable and X = −ln(1 − U). Find the PDF, CDF of random variable X.…
A: Here, it is provided that a random variable U has uniform distribution over 0,1. Another random…
Q: If X is an exponential random variable with PDF fX( x ) = a exp ( − ax ) for x ≥ 0, where a =0.8.…
A: X is an exponential random variable with PDFfX( x ) = a exp ( − ax ) for x ≥ 0
Q: Suppose X and Y have joint probability density function 1/2 if 0 < x < 1, 0 < y < 1, 1/3 if−1 < x <…
A: Let X and Y be the continuous random variables with pdf f(x,y) given asTo find:a) The value of Cb)…
Q: C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ =…
A:
Q: Q5. Let's assume X is a random variable which represents the number of years in which randomly…
A: Given, total frequency = 500 16+p+189+115+q = 500 p +q = 180 ....(1)
Q: Let X ∼ U(a, b). Use the definition of the variance of a continuous random variable (Equation 2.38…
A: The mean of X is given by:
Q: Consider a random poker hand of 5 cards. Let X be the number of Hearts in this hand, and let Y be…
A: There are 13 hears, 13 diamonds and 26 cards that are neither hearts or diamonds in a deck of 52…
Q: C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ =…
A:
Q: Y is an exponential random variable uith var [y]<25 what i's the PDr of y? what is the ELY]? what is
A: Given that Y is an exponential random variable. And, varY=25 Exponential distribution: A random…
Q: A random variable X is normally distributed with a mean of 100 and a variance of 100, and a random…
A:
Q: 2. Let X represents the lifetime of water turbine in years. The lifetime of the turbine is a random…
A: f(x)=ke-0.5x ; x>0
Q: Q.4 a. b. C. X is uniform in [0,4] and Y= 4logel4/X) What is the pdf of Y? What is the mean of Y?…
A: Q4. Given that random variable is uniform in ,so it's probability density function is the…
Q: When you post a picture on social media, it seems like your friends randomly "like" the picture.…
A: The question is about discrete prob. distribution Given : Prob. of the picture being " liked " ( p…
Q: Let Ybe an exponentially distributed random variable with mean ß. Define a random variable X in the…
A: Y is an exponential random variable with mean β . Therefore, the PDF of Y is:Result:∫eaxdx=eaxa
Q: Let X - T(25). Find P30(X) (30th percentile of X)
A: Solution: From the given information, X follows T distribution with degrees of freedom 25.
Q: Suppose that a random voltage V supplies a random current I through a constant resistive load. What…
A: The correlation between the random variables V and I is given by ρV, I=CovV, IVarV·VarI.
Q: let Y be a random variable that can either be equal to 0 to 1. let p(Y=1)=p,what is E(|Y-p|)?
A:
Q: A random variable X has P(5<X<19) 2 0.75. Using Chebyshev's theorem, the mean and variance (H, o2)…
A: The mean will be the average of 5 and 19. So, mean= (5+19)/2=12
Q: Consider the function ln (x). a. Normalize it so that it is a PDF on [2.80, 6.76]. b. Compute the…
A: The function given is ln(x). The function needs to be normalized. A normalized function has…
Q: Derive the mgf of an exponentially distributed random variable with mean β. Verify that(E[Y])2 =…
A:
Q: If random variable x is exponentially-distributed with mean a= 2, calculate p(X> 3)· Σ 2e-2x x=3 E…
A: From the provided information, Mean (λ) = 2 X~exp(2)
Q: 2. Consider the function ln x. a. Normalize it so that it is a PDF on [2.77, 4.38]. b. Compute the…
A: see the attachment
Q: f X is a random variable such that: E(X) = 6.2 and E(X2) = 62.5, then what is the standard deviation…
A: Given: X is a random variable. E(X)=6.2 E(X2)=62.5
Q: Suppose the random variable X has pdf K exp 12V/28 XP ( - ("=2)²). fo 2√/2K 0. £x(u) = 0≤u≤ 4,…
A:
Q: Let x, and x, be independent random variables with respective means µ = 75 and µ = 50, and standard…
A: 1) Given that W=x1-x2So, mean…
Q: Let X ~ U (a, b). Derive X mean and variance. Use the method of moments to construct an estimator…
A: Given, X~U(a,b) Then pdf is
Q: Let Y₁, Y₂, .. with mean 0. Yn denote a random sample from an exponential distribution a. Show that…
A:
Q: Consider an estimator of μ: W= 1/6 Y1+1/16Y2+1/4Y3+1/8Y4+1/2Y5 This is an example of a weighted…
A: Estimation and Estimator: When we are concerned in finding numerical values of unknown parameter(s),…
Q: For a random variable X, you are given: E[2*] = e#(z-1) Determine the coefficient of variation of X.
A:
Q: Suppose that a random variable X has the following moment generating function, Mx (t) = (1-9t)−7, t<…
A:
Q: Given X and Y are two events. LetP(M) = 0.49, P(N) = 0.44, P(MN) = 0.17 Find the value of…
A: M,N are two events.P(M)=0.49P(N)=0.44P()= 0.17we need to find P(M/N')
Q: Suppose that Y is an exponential random variable with λ = 4. Find. P[Y > (E(Y) + 2√√Var(Y))].
A: From given data we have : λ=4 and Y~exp(λ)
Q: Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the…
A: The given pdf is shown below:
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 5 images
- The variance of Y is σ2y = 4.6875 and the variance of the sum is σ2x + y = 9.1875. You knowthe variance of X=1. Find the covariance, xy. Show workFind the value of k which make the following function a pdf (15 y - 2 sys0 64' 64 fW) ={ 3 + ky 0 < y< 3 8 elsewhere What is the P(-1 < Y S 2)? Find the cumulative distribution function of Y. Find the variance of Y.Given pdf f (x) = 1.5x2 for −1< x < 1. Determine variance of X.
- Let X₁, X2,..., be a sequence of independent and identically distributed random variables, each with a mean value x and variance ok, both of which are assumed to be finite. Let N be a discrete random variable independent of X₁, X2,..., and assuming values in the set {0, 1, 2, ...}, with mean value N and variance ok (both are finite). Form the random-compound sum Y=1 Xk, with the convention Y = 0 whenever N = 0.Let X be a normal random variable with mean 85 and a variance of 25 (i.e., X ∼ N (85, 25)). step1: Let M = aX + b for some constants a, b not equal to 0. Write an expression for the pdf of M . step 2: Suppose that X represents an approximate distribution of the final scores in a certain math course (ignore the fact that this approximation can technically have scores that are greater than 100 or less than 0). If the teacher were to curve the scores, it means he would determine a function to apply to the scores to achieve a desired distribution (assume an affine function in this case, as in the previous part). Suppose he wants the scores to be normally distributed with mean 80 and a standard deviation of 4. What should he choose for a and b? What students would see their score lowered, and what students would see their score increased?Let Y be a random variable with pdf f(y)=(3/64)y2(4-y), Osys4, zero elsewhere. Match the following. A. 0.31 B. 12.2 C. 16 D. 2.40 E. 0.64 select 1. E(Y)= select 2. V(Y)= select 3. Let X=3Y+5= E(X)= select 4. Let Z-5Y+3= V(Z)= select 5. P(YS2)3
- Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information. Σχ - 64.2; Σ ? = 528.24; Ey = 90.4; Ey² = 1063.88; Exy = 741.77 6.2 8.6 7.0 7.5 8.3 6.9 10.0 9.7 y 9.7 10.3 10.9 11.5 14.2 7.0 14.6 12.2 Find the equation of the least-squares line. (Round your answers to three decimal places.) Find the sample correlation coefficient r and the sample coefficient of determination r. (Round your answers to three decimal places.) r = 2 = If x = 7.0, use the least-squares line to predict y. (Round your answer to two decimal places.) y = Find an 80% confidence interval for your prediction. (Round your answers to two decimal places.) lower limit mg/10 ml upper limit mg/10 ml Use level of significance 1% and test the claim that the…Kelvin’s bookcase holds 2 algebra books, 1 calculus book, and 4 geometry books. Books are taken at random from his bookcase, one after another and without replacement, until a geometry book is had, at which point no more books are taken. The random variable Y represents the total number of books taken during this experiment. Find Pr[ Y = 3 ].Let X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The covariance of x and y is 0.35. Let Z=4X – 5Y+2. What is the mean and variance of Z?
- Let A and B be independent exponential random variables, both with mean 1. If U = A + B and V = A/B, find the joint pdf of U and V.4. Suppose that X has pdf f(x) = 3x² for 0 < x< 1. Find the pdf of the random variable Y = VX.Assume that McDonalds can serve a customer's order in X minutes after the customer enters the fast food chain. The PDF of the random variable X is shown as: 0.1 10 Moreover, assume that the customer can finish the food Y minutes after it is served, independent of the serving time. The PDF of the random variable Y is shown as: i. ii. |fx(x) 0.1 fy(y) fy(y) = 0.1e-0.1y 50 Let Z = X + Y be the total amount of time that the customer stays inside the fast food chain. 15 20 What is the probability that the customer stays within McDonalds for at most 18 minutes, i.e. P(Z < 18)? What is the expected value (in minutes) that the customer stays within the fast food chain?
