2. Let X be a continuous random variable with pdf ca2, 1 f(x) otherwise, where the...
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 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).
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).
LI CONTINUOUS DIST Let X be a random variable with pdf -cx, -2<x<0 f(x)={cx, 0<x<2 otherwise where c is a constant. a. Find the value of c. b. Find the mean of X. C. Find the variance of X. d. Find P(-1 < X < 2). e. Find P(X>1/2). f. Find the third quartile.
(22pts) 6. Suppose X is a continuous random variable with the pdf f(x) is given by $(x) = { 1 + 2 OSIS 1; Osasi otherwise. (4 pts) a Verify f(x) is a valid pdf. (4 pts) b. Find the cumulative distribution function (cdt) of X (4 pts) c. Find P(OSX30.5). (5 pts) d. Find E(X). (5 pts) e. Find V(x)
(b) Let X be a continuous random variable with pdf given by: f(x) =c#x Find the constant c so that f(x) is a pdf of a random variable. C (ii) Find the distribution function F(x)P(X Sx)X (ii) Find the mean and variance of X. .Col니loa, ,iaaa4
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1
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)
3. Let X be a continuous random variable with the following PDF f(x) = ( ke 2 x 20 f(x)= otherwise where k is a positive constant. (a). Find the value of k. (b). Find the 90th percentile of X.
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].