Let X be a discrete random variable with pmf p given by: -2 -1 0 1 2 1/15 2/15 3/15 4/15 5/15 X p(x) (a) Let Y = X². Find the pmf of Y. (b) Find the value the cdf of X at -1/2, 3/4, 7/8, 1, 1.5, 5. (c) Find the value the cdf of Y at -1/2, 3/4, 7/8, 1, 1.5, 5.

Q: 1 The discrete random variable X has Var (X) = 5 Find Var (4X – 3)

A: Given Data: Var(X)=5 Equation: Var(4X-3) ......(1) Simplify the equation (1). Var4X-3=42VarX=16VarX

Q: Let u(X) be a nonnegative function of a random variable X. It can be shown that  P(u(X) >= c) = a)…

A: It is an important part of statistics. It is widely used.

Q: For the random variable X, E(X+1) = 3 , E(X- +X)= 9 then the value of Var(X) is 10 3 0 2 0 50

A: Given, E(X+1)=3 Then E(X)+1=3          E(X) =2 and E(X2+X)=9       E(X2)+E(X)=9       E(X2)+2=9…

Q: Let X be a random variable with E(X)= 1 and E[X(X-1)]=4,then evaluate Var(2-3X).

A:

Q: For a uniform random variable U∼U(0,14)U∼U(0,14), find the probability P(U>11)P(U>11): P(U>11)

A: From the provided information, U~U(0, 14) a = 0 and b = 14

Q: Let X(n,p) denote a binomial random variable with parameters n and p. Show that X(n+1,p)>=st X(n,p).

A: Given To prove that

Q: A9. Let X and Y be independent standard normally distributed N(0, 1) random variables. What is…

A: Given that  X and Y are independent standard normal distribution N(0 , 1).

Q: Let X be a discrete random variable with pmf (a) Find the pmf for Y = X². (b) Find the pmf for U = X…

A: The PMF of random variable X is: f(x)=18      x=-214      x=-114      x=014      x=118       x=2  0…

Q: Suppose a random variable has a CDF given by Fx(x) = (1-e-x)u(x). Find the following quantities: (a)…

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted....…

Q: X and Y are random variables that are both Normally Distributed. The Mean of X is 5 and its SD is 3.…

A: Given that  P(4 < Y < 16) = P(A < X < B) μX=5σX=3μY=-2σY=6

Q: A coin is tossed 3 times and then a die is rolled. Let X be the number of heads times the number of…

A: Given that A coin is tossed 3 times and then a die is rolled. Let X be the number of heads times the…

Q: Let Y be a discrete random variable with generating function 4 Gy (s) 6 - s s2 What is E(Y) (in…

A: