Suppose X is a random variable with probability mass function f(x) = k if x =...
Suppose X is a random variable with probability mass
function
Find k.
A. 9/80 B. 11/20 C. 9/20 D. 18/50 E. none of the preceding
f(x) = k if x = 0 3k if x = 1 11/20 if x = 3
3. A random variable X has the probability mass function P(x = k) = (a > 0, k =0,1,2...). (1 + a)! Find E[X], Var(X), and the Moment generating function My(t) = E[ex]
Suppose that the probability mass function for a discrete random variable X is given by p(x) = c x, x = 1, 2, ... , 6. Find the value of the cdf F(x) for 3 ≤ x < 4.
4. Suppose that X is a random variable having the following probability distri- bution function - 0 if r<1 1/2 if 1 x <3 1 if z 2 6 (a) Find the probability mass function of X. (b) Find the mathematical expectation and the variance of X (c) Find P(4 X < 6) and P(1 < X < 6). (d) Find E(3x -6X2) and Var(3X-4).
Let X have probability density function f(2)= k(1+x) -3 for 0 < x < oo and f(x) = 0 elsewhere. a. Find the constant k and Find the c.d.f. of X. b. Find the expected value and the variance of X. Are both well defined? c. Suppose you are required to generate a random variable X with the probability density function f(x). You have available to you a computer program that will generate a random variable U having a U[0,...
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
The random variable X has probability density function f (x) = k(−x²+5x−4) 1 ≤ x ≤ 4 or =0 1 Show that k = 2/9 Find 2 E(X), 3 the mode of X, 4 the cumulative distribution function F(X) for all x. 5 Evaluate P(X ≤ 2.5). 6 Deduce the value of the median and comment on the shape of the distribution.
Suppose density function positively valued continuous random variable X has the probability a fx(x)kexp 20 fixed 0> 0 for 0 o0, some k > 0 and for (a) Find k such that f(x) satisfies the conditions for a probability density function (4 marks) (b) Derive expressions for E[X] and Var[X (c) Express the cumulative distribution function Fx(r) in terms of P(), the stan dard Normal cumulative distribution function (8 marks) (8 marks) (al) Derive the probability density function of Y...
A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer. a. Find the constant k. b. Find the expected value M(S) = E(esX) as a function of the real numbers s. Compare the values of the derivative of this function M'(0) at 0 and the expected value of a random variable having the probability function above. c. What distribution has probability function f(x)? Let X1, X2 be independent random variables both...
Consider the discrete random variables X and Y with the following joint probability mass function: 2 y fxy(x,y) -1 0 1/8 0 -1 1/4 0 1/4 0 1/8 -1 1/8 1 -1 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 1 1 1 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding 3. Multiple Choice Question Suppose that the number of bad cheques received by a...