Suppose a random variable X has the density function fx (x) if x 1 and 0 otherwise. If Y = X+2, then what is fy (4) ? Answer either as an integer or as a simplified fraction.

1. A continuous random variable X is defined by (3+x) f(x) - 3sxs-1 %3D 16 (6-2r) -1sxs1 16 (3-x) -1sxs3 16 a. Verify that f(x) is density. Explain b. Find the mean 2. If the probability density function of random variable is given by f(x) = wch 1srs2 sech x a. Find the mean b. Find the total area 3. If the probability density function of random variable is given by f(x) = sinh 2x 1sxs2 a. Find the mean b. Find the total area c. Illustrate the graph (use bell shaped figure) II II

Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.03. Suppose that on a given day io patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: E(X)=0.4 and V(X)=0.384 O None of these O E(X)=0.5 and V(X)=0.475 O E(X)=0.3 and V(X)=0.291

2. If the random variable X has the probability density function f(x) = (1-x²), -1 < x < 1, 3 4 what is the variance of 15X + 2?