Given the CDF Fy(9) of random variable Y 1 0.8 0.6 0.4 0.2 0 1 2 3 4 5 y Is Y discrete or continuous? Explain. Plot the PMF/PDF of random rariable Y (whichever is applicable). What is the value of P[1 < Y < 4]?

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: (1) Find the value of k which make the following function a pdf fly) = { (15/64) +(y/64) -1<= y <= 0…

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Q: A random variable Y has a uniform distribution over the interval (?1, ?2). Derive the variance of Y.…

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Q: Let Xi, X2, f(x;e)- ee *I c0.00 (x). Find a l00y or percent confidence interval for the the…

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Q: (b) The CDF F(x) of a random variable X is given by; if x 3 (i)find PDF f(x) (ii) P(|X| < 1.5),…

A: The P.D.F is given by: fx=ddxFx=ddxcx-14=4cx-13

Q: EX7.8) Let Y be a random variable having a uniform normal distribution such that Y~U (2,5) Find the…

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Q: Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y…

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Q: A Gaussian random variable with variance 10 and mean 5 is transformed to Y=e. Find the pdf of Y.

A: Solution-: Given: μ=5,σ2=10 Let, Y=eX Find pdf of Y?

Q: Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 =

A: We want to findvalue of t

Q: 5. Let X have the pdf {(x + 1) -1 <x < 1 f(x) = elsewhere. Find the mean and the variance of X.

A: 5. The given pdf is, fx=12x+1       -1&lt;x&lt;10                   elsewhere

Q: fx(x) = {{ √ x/2 01 Let Y be the output of the "clipper": Find: a) The probability P[Y = 0.5] b) The…

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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: Suppose that the pdf of a random variable is given by f(y)=1/10 , -5<y<5 For what value of y does…

A: It is given that, the pdf of a random variable is given by f(y)=1/10, -5&lt;y&lt;5

Q: Prob. 3 Let X be a random variable with cumulative distribution function (cdf) given by Fx(x) = {1 -…

A: Let X be a random variable with a cumulative distribution function (cdf) given byTo findThe…

Q: (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X.

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Q: Let X have a mean of 132 and a variance of 32. Define Y=X² + 2X+1. Compute the (a) mean and (b)…

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Q: 1 0.8 2 0.6 0.4 0.2 0 1 3 4 y A.Is Y discrete or continuous? Explain. Plot the PMF/PDF of random…

A: Solution

Q: The CDF F(x) of a random variable X is given by; F(x) = { 0, if x 3 } (i)find PDF f(x) (ii) P(|X| <…

A: (i) fx=dFxdx                                  for 1&lt;x≤3=dcx-14dx=cdx-14dx=4cx-14-1=4cx-13…

Q: Find the MGF of the binomial distribution ()ra- Use it to show that the mean is p and the variance…

A: Given that the pmf of the binomial distribution is P(X=x)=nxpx1-pn-x, x=0, 1, 2,..., n. We have to…

Q: (Y-1)². Use one decimal place accuracy.

A: Given that  Y ~ Uniform (1 , 11)

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: If X is a Gaussian random variable with mean zero and variance o, find the pdf of Y = \XI.

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Q: Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete…

A: For the given data Find the covariance and correlation between x and y

Q: Let X Poisson(A) and Y = vX. Use the delta method to approximate the mean and variance of Y.

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Q: Assume that ξ has a rectangular distribution with the mean value E(ξ) = 0 and the variance V(ξ) =…

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Q: Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the…

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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:

Q: The mean and variance of a Binomial variable X with parameters n and p are 16 and 8. Find P(X> or =…

A: Given: X ~ Bin (n , p) EX=16VX=8

Q: Consider a random sample from the distribution of Binomial, Poisson, Exponential, Gamma, and normal.…

A: Let Xi~Bn,p, the the p.m.f of Xi is given by, px=Cnxpxqn-x,x=0,1,2,...,n Then, EXi=np and VXi=npq…

Q: 1. Let X be a random variable with pdf f(x) = 1,0 3).

A: The random variable has pdf is given by:

Q: Let X be a random variable with p.d.f f(x) =x(9-x), 0sxS 3. Find the mode.

A: Introduction Mode: Mode is one of the types of measures of central tendency. Mode is the location…