(52) Let X be a random variable with p.d.f. 1 5 0

Q: (17) Let X be a random variable with p.d.f. o >x>0 f(x)=< find E(e) O.w

A: Solution : Given :  f(x) = 15e-15x          0&lt;x&lt;∞0           o.w Here X ~exp(15) M.G.F of x is…

Q: 12 Let X be a random variable with mgf(t) = 0.6e' + 0.3e2t + 0.1e3t Find E(X) For the instructor,…

A:

Q: Find the E(X) of the random variable X with the following PDF: £x(x)=4410.11(x)+(1.2)(x)+(-+)423)(x)

A: 3 Given density function is, fx=x2I0,1x+12I1,2x+-x2+32I[2,3)x      =x2, 0&lt;x&lt;112,…

Q: Consider the random variables X, and Y₁ from question B1 again. (a) Show that the sample covariance…

A: a) Recall that the sample covariance between X and Y is defined as: Cov(X,Y) = 1/n * ∑(Xi - x̄)(Yi -…

Q: 2. A random variable X has pdf |x| < 1 elsewhere. cx(1+ x) a. Find c. b. Find E{X}and V AR{X} c.…

A:

Q: Given a random variable X with anf(x) = x between 0 and 1, with an f(x) = x/3 between 1 and 2, and…

A: The probability density function (PDF) of the random variable  is given by,

Q: A random variable, x, has p.d.f. f (x) given by f (x) = 1 а. always equals 1 b. 0 < x< 1 C. Not…

A: We know that,  If a random variable x having probability density function f(x) by the property of…

Q: The cumulative probability distribution for the random variable X 0, x<0 F(x)= 8 3x2 Osx<2 given as.…

A:

Q: 8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable…

A: The objective of the question is to find the probability that the time taken by a mechanic to…

Q: Find E (X) and E(X²) and using these values evaluate E[(2X + 1)²]

A:

Q: Problem 5. (i) Let X be a random variable such that log X is normally distributed with mean u and…

A: Find  (i) P(X&lt;a)=? (ii) find the distribution of ∑Xi

Q: f(x) -a ey, x > 0, and 0 otherwise. 1 Given that i. Show that f(x) is a distribution fX is a random…

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Q: 2.2 Let the variable X have the binomial distribution, that is, p(x) = (") p*(q)"-*, x = 0,1,2,-,n…

A:

Q: 2.3. Let X and Y be random variables and let A be an event. Prove that the function Z(w) = is a…

A: We know that,A random variable is a numerical description of the outcome of statistical experiment.…

Q: 4.4.26. Compute P(Y, < fo.5 <Y;) if Y1 < < Yy are the order statistics of a random sample of size 9…

A: It is given that Sample size n = 9 Yi, i = 1,2,......,9 are order statistics.

Q: a) The discrete probability distribution is given by 0 1 2m X P(X = x) m i. ii. iii. Calculate…

A: From the provided information, x 0 1 2 3 P (X = x) m 2m 3m 2m

Q: Let X be a random variable with p.d.f. x = 1,2,3 f(x) = { find (1) k (2) E(x²) O.W

A: Solution: 36. From the given information, the probability density function of X is

Q: Consider an exponential random variable X with pdf f(x | θ) = θ −1 e −x/θ, x > 0. A single…

A: (a). Compute the probability of committing a Type I error: It is given that, a random variable X is…

Q: (1) E(E(X)) = E(X) (2) E(X – E(X)) = 0 (3) Var(X) = E(X²) – [E(X)]² (4) Given constants a and b,…

A: Discrete random variable is defined as a variable which can take only specific values. For example…

Q: 6. Suppose we have the cdf of a continuous distribution with random variable X given by the function…

A: Calculation Part: 6) The cdf of X is given by F(X)=0,                           for x&lt;0…

Q: 9. A random variable X has the following p.m.f: X0 1 2 3. P J0.1 0.3 0.4 0.2 And F(x) is the cdf for…

A: It is given that the, A random variable X has the pmf as X P(X=x) 0 0.1 1 0.3 2 0.4 3 0.2…

Q: 8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable…

A: The objective of the question is to find the probability that the time it takes a car mechanic to…

Q: Let X be a discrete random variable with the following PMF: for x = 0 Px(x) = = 12 L3 L6 for x = 1…

A: Step 1:The probability mass function is given asx012P(x)1/21/31/6The range of the given PMF would be…

Q: Let X be a random variable distributed exponentially with parameter such that is 1/2 find the…

A:

Q: [30p] 1. The sample space S of a random experiment is given by S = {a, b, c, d, e, f, g} and !3! let…

A:

Q: The moment-generating function of the discrete random variable X is M(t) = 1.21 e+ 6 What is the…

A: Given Data: Moment generating function: Mt=13e-2t+16+16e2t+13e-3t ......1 Let, P(x) is the…

Q: 8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable…

A: The objective of the question is to find the probability that the time taken to replace a car…

Q: 1. Let X be a Gaussian random variable with mean 6 and standard deviation o? = 10. Find (a) P(X> 6)…

A:

Q: 1. Suppose the PMF of the random variable X is px(x) = .21(1.3)(x) +.61(2)(x). What is the mean of…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A discrete random variable, X, has the following pdf as follows. X 0 1 2 3 4 P(X = x) 0.15 0.3 a 0.2…

A: Step 1: Given table, pdf tablex01234P(X = x)0.150.3a0.20.1 Step 2: a) The value of 'a' can be…

Q: v.2.J Assume the random variable x is normally distributed with mean u= 50 and standard deviation o…

A: Obtain the standard z-score for the random variable equals 43. The standard z-score for the random…

Q: Compute P(X< 5)

A: We have to compute P(X &lt; 5) for the given density function of the random variable X.

Q: 0. Let X be a non-negative discrete random variable. Prove that E(X) = | (1-F(2)) dæ 0,

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Q: 1. Suppose the PMF of the random variable X is px(x) = .21(1.3)(x) + 6(2)(x). What is the mean of X?…

A: The question is about expected value of a discrete random variable Given : Pair of fair dice is…

Q: Hom variable X has the gamma p. d. f with integer j rary ß>0, then E(Xk) is

A:

Q: Q4/ a. Find areal root of the equation f(x) = e* - 2 = 0 (Using False Position Method in four…

A: Solution:- Question 4(a) Here , ex-2=01st iteration :Here f(0)=-1&lt;0 and f(1)=0.7183&gt;0∴ Now,…

Q: 14. Let X be a discrete random variable with the following PMF 1 for k = -2 4 1 for k = -1 Px (k) 1…

A: Farmula used  Range=Maximum-Minimum

Q: (i) Show that c = 2 (ii) Calculate the mean and variance of X. (iii) Find the CDF of the random…

A: As per policy I have calculated first 3 subparts plz REPOST for remaining parts with note I need…

Q: Let A be the mean of the random sample drawn from a population whose pdf is given by fox =…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: For a random variable X, you are given: E[2*] = e#(z-1) Determine the coefficient of variation of X.

A:

Q: Q. 2 For the exponential random variable X with parameter à = 2, compute the ollowing probabilities.…

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Q: 1) Determine the value of c. 2) Find (a) P{|x| < 1}, (b) P{X² < 9}, and (c) P{X = 1}

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Q: E. Alex is back on Tinder. Let X, be a random variable that is equal to 1 if i-th person is a match…

A: Here, Xi's are Bernoulli trials which takes values either 0 or 1, with p = 0.50. Mean and standard…

Q: b) The continues random variable has the following probability density function; 0<x <4 12 f(x) 2<x…

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')

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!