1. Let X1, X2, X3 be identically distributed independent exponential random variables and Y = X₁+ X2 + X3. Suppose that EY4 = 480. Find the probability P(X2> 3|X1 <1).
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- Let X,, X2, and X3 be independent random variables, each are binomially distributed with n = 100 and p = 0.2. Let A = X,– 2X2 and B = X3 + 3X1. Find PAB- %3D %3DA- Let x be a discrete random variable with probability distribution function f(x)=k( x2 +20) and x= −1,1,2,3. Find the value of k. Find the Variance of X. B- Let x denote a discrete random variable which can take the values −2,0, and 5. Given that the expectation of X is 8/100 and P(X=−2)=8/20 , find P(X=5).IfX is a random variable that has a uniform distribution on the interval [o, 10), then PX+ 10 27 is equal to
- Q2) Suppose that X is a continuous random variable with probability distribution £x(x) = ₁ 0≤x≤4 Find the probability distribution of Y = (x - 2)².let x be a discrete random variable with probability function p(x)= cx/20 for x = 2,3,4,5,6,8,12 what is the value of c that makes p(x) a valid probability function?Suppose a and b be two possible values of a random variable X with a > b. The probability that X lies between a and b is P(a > X > b) = F (a) - F (b) Select one: O True O False
- Let X and Y denote two random variables. Which of the following can be used to compute Var(X)? A. E[Var(X|Y)] + Var(Var(X|Y)) B. E[E[X|Y]] + Var(Var(X|Y)) C. E[Var(X|Y)] + Var(E[X|Y]) D. Var(E[X|Y]) + Var(Var(X|Y))The possible values of a discrete random variable X are 0, 1, 3, and 6 with respective probabilities 0.2, 0.3, 0.1, 0.4. Find E[X] and Var(X).Let X and Y be two random variables such that Cov(X.Y) = -3 . Then %3D O None of these O cov(-3X+5,-3Y+5)=-18 cov(3X+5,-2Y+5)=18 O cov(5X+3,-2Y-2)=-20
- a.2 b.-1 c.0 d.-2 e.1X has been defined as the Poisson random variable. Thus, P (X = 1) = 0.149 and P (X = 2) = 0.224 are given. Find out what the probability P (X = 0) is.Each of the random variables X and Y takes only 3 values {1,2,3} with the following probabilities: 1 1 0 1/6 1/6 y 2 1/6 0 1/6 3 1/6 1/6 0 2.