Suppose X is a continuous random variable having pdf (1+x, -1 < x < 0, f(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)
Example 46. Let X be a random variable with PDF liſa - 1), 1<a < 3; f(a) = { à(5 – a), 3 < x < 5; otherwise. Find the CDF of X. @ Bee Leng Lee 2020 (DO NOT DISTRIBUTE) Continuous Random Var Example 46 (cont'd). Find P(1.5 < X < 2.5) and P(X > 4).
5. Y is a continuous random variable with pdf f(y) = (4 – y)/8, 0<y< 4. (a) Find E(Y). (b) Find E(Y2). (c) Find Var(Y).
(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.
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.
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)
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 <
4B-03] Suppose that we are given the random variable X with pdf f(x) = 1-x/2 for 0<x<2, and 0 otherwise. Obtain P(X1). (Round to 2 decimals) Your Answer: Answer
8. Suppose X is a continuous random variable with density f(x) = 1/3,-1 < x < 0, f(x) = 2(z-1)2,1 < x < 2, and 0 everywhere else. (a) Find E(X).
1. Suppose X and Y are continuous random variables with joint pdf f(x,y) 4(z-xy) if = 0 < x < 1 and 0 < y < 1, and zero otherwise. (a) Find E(XY) b) Find E(X-Y) (c) Find Var(X - Y) (d) What is E(Y)?