4. et X be a continuous random variable with support (0, 2) and PDF defined by f(x) = ( cx3 0 < x < 2 0 otherwise. a) Compute E[X]. b) Compute V ar(X)
4. et X be a continuous random variable with support (0, 2) and PDF defined by...
1. Let X be a continuous random variable with support (0, 1) and PDF defined by f(x) = ( cxn 0 < x < 1 0 otherwise, for some n > 1. a) Find c in terms of n. b) Derive the CDF FX(x).
2. Suppose that the continuous random variable X has the pdf f(x) = cx3:0 < x < 2 (a) Find the value of the constant c so that this is a valid pdf. (10 pts) (b) Find P(X -1.5) (5 pts) (c) Find the edf of X use the c that you found in (a). (Hint: it should include three parts: x x < 2, and:2 2) (20 pts) 0,0 <
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1, f() = 0. Otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(2) of X. (c) Use F(2) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
3.17 A PDF for a continuous random varaiable X is defined by C 0<x<2 2C4<< 6 fx(x) = 3 C 7<<<9 0 otherwise where C is a constant. (a) Find the numerical value of C. (b) Compute Pr[1 < X < 8). (c) Find the value of M for which "fx(s)de = [fx (a)dr = 1 J-00 Mis known as the median of the random variable.
2. Let X be a continuous random variable with pdf ( cx?, [xl < 1, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2. Let X be a continuous random variable with pdf ( cx?, |a| 51, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
Suppose X is a continuous random variable having pdf (1+x, -1 < x < 0, f(x) = { 1 – x, 0 < x <1, lo, otherwise (a) Find E(X2). (b) Find Var(X2).
2. Let X be a continuous random variable with pdf ca2, 1 f(x) otherwise, where the parameter c is constant (with respect to x) (a) Find the constant c (b) Compute the cumulative distribution function F(x) of X (c) Use F(x) (from b) to determine P(X 1/2) (d) Find E(X) and V(X)
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)