5. Determine the expectation of the random variable whose density function is given in problem 2. 6. Determine the variance of the random variable whose density function is given in problem 2. 2. Let X be a continuous random variable with probability density function f(x) = 1 π[1 + (x − 1)²] - for-co< x < ∞o. Find the cumulative distribution function.

Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .

. Find the expected value of the Probability density function: ƒ(x)= 24 (3x)(4 — x) - 64 on the interval of [0,4]. Then find V(x), and o

Let X and Y be independent random variables with joint probability density function fxy(x, y) = 1/3 (x + y), 0 < x <= 2, and 0 < y<= 1, and 0 otherwise. The marginal pdf fx(x) is given by O a. O b. O c. O d. (2 +2X)/3 (2 + 2X)/3 (X+1/2)/3 (X+1/2)/3 0 < X<= 2 0< X<= 1 0 < X<= 1 0