4 A coin is biased so that the probability of obtaining a tail is 0.75. The coin is tossed four times and the random variable X is the number of tails obtained. Find (i) E(2X) (ii) Var(3X). 11

J and K are independent events. P(J | K) = 0.23. Find P(J)

X P(x) =C p*q"-x %3D When processing credit-card applications there is a 40% chance that an application will have incomplete or insufficient information and require research. You have 5 applications in your to-do pile and would like to leave early today. (a) Fill in the values: n = q = (b) What is the probability of exactly three applications needing research? (enter a number between 0 and 1, 4 decimal places) Answer= (c) What is the expected number of applications that will need research? Answer= (d) What is the probability of having AT LEAST the expected number of applications needing research? (enter a number between 0 and 1, 4 decimal places) Answer= Please answer all parts of the question.

J and K are independent events.  P(J|K) = 0.6.  Find P(J).