2.6.11. Adegenerate random variable is a random variable taking a constant value Let X= c. Show...
1. 20 points Let X be a random variable with the following probability density function: f(x)--e+1" with ? > 0, ? > 0, constants x > ?, (a) 5 points Find the value of constant c that makes f(x) a valid probability mass function. (b) 5 points Find the cumulative distribution function (CDF) of X.
3. (8 pt, 2 each) (Ross) Let X be a random variable taking values in the finite interval 0, c]. You may assume that X is discrete, though this is not necessary for this problem (a) Show that EX c and EX2 cEX (b) Use the inequalities above to show that Var(X) <c2[u(1-u)] u=EXE[0, 1]. where (e) Use the result of part (b) to show that Var(cx) se/ (d) Use the result in (c) to bound the variance of a...
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm 5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
Please help with this question. 12. (15 points) Let X be a continuous random variable with cumulative distribution function 0. F(x) = Inc. <a a<x<b bcx 1. (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
Let x be a random variable with the following probability distribution: Value x of X -2 - 1 0 0 0 1 0 P(X-X) 0.10 .30 .20 .40 Find the expectation E (x ) and variance Var (x) of X. (If necessary, consult a list of formulas.) ( x 5 ? Var (x) - 0
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
Let X be a random variable with the following probability distribution: Value x of X 40 50 60 70 80 P(X=x) 0.05 0.25 0.10 0.30 0.30 Find the expectation E (X) and variance Var (X) of X. (If necessary, consult a list of formulas.) x 6 ? E (x) = 0 Var(x) = 0
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a Inz, a<<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function S(x) for X. (d) Find E(X)
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a F(x) = Inr, asi<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(x > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
(15 points) Let X be a continuous random variable with cumulative distribution function F(x) = 0, r <α Inr, a< x <b 1, b< (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)