Hawassa University IOT Probability and Random Process Assignment 2024 PDF

Hawassa University IOT Probability and Random Process Assignment II( Group work max 5 Student). Random variable X is called an exponential r.v. where its pdf is given by  1 x/  e , x  0, f...

Hawassa University IOT Probability and Random Process Assignment II( Group work max 5 Student). Random variable X is called an exponential r.v. where its pdf is given by  1 x/  e , x  0, f X ( x)     0, otherwise. a) Find the cdf of X. b) Find the mean and the variance of X. Two caplets are selected at random from a bottle containing three aspirin, two sedative, and four cold caplets. If X and Y are, respectively, the numbers of aspirin and sedative caplets included among the two caplets drawn from the bottle, find the probabilities associated with all possible pairs of values of X and Y Let the joint density of two random variables x1 and x2 be given by Find E[x1], E[x2], E[x1x2] and Cov (x1 x2) They random variables X and Y are jointly distributed over the region 0 < x < y < 1 as 0< <