(a) V is a Gaussian (u= 0, o = 2) random variable. Find P[V> 4]. (b) W is a Gaussian (µ variable. What is PW< 2? = 2, 0 = 5) random (c) For a Gaussian (r, o = 2) random var- iable X. find PLX < +1]. (d) Y is a Gaussian ( = 50, a = 10) ran- dom variable. Calculate P(Y> 65].

Q: The joint probability densíty function of the lar random variables, up fx,y (xiy)= cx,0<y<x<1,44…

A: f(x,y) = cx , 0 &lt;y&lt;c&lt;1.44   a) We know that,

Q: (6) Let X be a Poisson random variable with parameter 0, then E(X²) = 1. От OF

A: Poisson distribution is the type of discrete probability distribution. It explain the number of…

Q: how to find E(X), E(Y), E(X^2)

A: Given that X and Y are independent and follows N(0,1)

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A: Given that both random variables X and Y are are independent. The mgf of X is:MX(t)=e2et-2By using…

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A:

Q: coefficient of correlation for Y₁ and Y₂. r answer to part (b) lead you to doubt your answer to part…

A: Answer:  Given joint probability distribution function of  is   (a) Let andbe jointly continuous…

Q: 12. Let X be a normal random variable with mean 678 and standard deviation 8.85. Let Q₁ the…

A:

Q: Let X and Y be independent and identical exponential random variables with parameter 0. Showthat Z =…

A: and represent  independent and identical exponential random variables.The parameterIt must be shown…

Q: QUESTION 2 Consider the following information about 3 random variables, X Y and Z. X|Y- Gamma(2Y2,).…

A: Given: X/Y ~ Gamma( 2Y2, Y) Y~ N(2, 5) From given: E(X/Y)=2Y2Y Var(X/Y)=2Y2Y2 We know that for…

Q: 5. (a) vNy Suppose that the age-at-death random variable T, is uniform in [0,w- x] with Var (T50) =…

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

Q: If 'b' is Constant and X be a Random Variable then VX +b)3V(X)

A:

Q: True or false. • (i) –1< Cov(X,Y) < 1. • (ii) Two random variables are independent if their…

A: Statement (i) is true.

Q: 7. If X is a random variable with fx Let Y = 3√In X. (a) Fx(x) ) = 1, 1<x<e (b) Fy(y) (c) fy(y)

A:

Q: Ex//let xa random variable with pm f p X=xN N , x=1,2,.., N and let Y=a+bx where a, bER find Ey and…

A:

Q: Suppose X~ Unif(0, 1). Let Y -2 ln(X). (a) Show that the random variable Y has a gamma distribution.…

A: The random variable  follows a uniform distribution with parameter  and .

Q: (6) Let X be a Poisson random variable with parameter 9, then E(X²) = 1.

A: Given X~Pois(θ)

Q: 4. For two independent random variables such that X sin N(0, 4), Y ~ U[0, 4], Var(2X +3Y) = Var(2X -…

A:

Q: 66. Consider two random variables X and Y with V(X) = 5, V(Y) = 10 and Cov(X,Y) = 3. (a) Find V(3X -…

A: V(X)=5 , V(Y)=10 and Cov(X,Y)=3

Q: (a) Show that the joint pdf for U, V is of the form f(x, y) = { exp(-u-v), if (u, v) E A otherwise…

A: We will use the method of Jacobian to determine the joint density of U and V.

Q: X is an exponential random variable with a mean of 5 and Y is a Rayleigh variable of second moment…

A:

Q: 1. Let the random variable Y have pdf as f(y\A) = e®=e=t(e-1), y>0,1>0. Show that W = e – 1] ~ x²…

A:

Q: F(x,y) = { (x+y)/42 ; x = 1,2,3  y = 1,2                 0; elsewhere ] (i) Find the mean for the…

A: F(x,y) : { (x+y)/42 ; x=1,2,3 y=1,2  ; 0 elsewhere } Mean : E(X) = sum(x*P(x))

Q: A continuous random variable has p.d.f. f(x) where { kx 0-x -1 f(x) - k(2-x) 1-x =2 otherwise Find…

A:

Q: px (k) = c( (4)* k for k = 1,2,3,.. 3. Let X be a discrete random variable with %3D 3 A. Find the…

A: A) The value of c is calculated as follows: ∑1∞c13k=1c∑1∞13k=1 c13+132+133+...=1 c31+13+132+...=1…

Q: Suppose that two independent and identically distributed random variables X and Y have common mgf…

A: Two independent and identically distributed random variables X and Y have common mgf:- MX(t) = MY(t)…

Q: 0 Find the marginal probability distributions of X and Y. otherwise a) b) Show that the two random…

A:

Q: 2. Let X and Y be two random variables. Suppose XY ~ Binomial (n, Y) where n is fixed and Y stands…

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Q: Example 2.7. Let X and Y be jointly continuous random variables with joint PDF is given by: fx,y (r,…

A: Solution

Q: 6) Consider the random variable Z₁ = cos (2 * π * Yn/n) where Yn is binomial(n,p) a. What is its…

A: This question considers a random variable Zn, which is defined as the cosine of 2π times a…

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Q: If X is a uniformly distributed random variable between -1 and 1 (pdf of x is constant=1/(2pi)…

A: From the given information, fx=12π, -π≤X≤π Given that Y=sin(X) Consider, the distribution function…

Q: X and Y are discrete random variables. If var(X)= var(Y) = o², cov(X,Y)= find var(2X-3Y)

A: