Let the Probability Mass Function as follows: f(-1)=0.2, f(2)=0.3, f(3)=0.35 and f(0)=??, Then F(2)= a. 0.35 b. 0.65 c 0.15 E0 P

For each probability expression, find the unknown z- value(s). Unless directed otherwise, use three decimals in your answers. (a) P(Z ≤ zo) = 0.86. Find zo. 20 (b) P(Z ≤ zo) = 0.24. Find zo. 20 = 20 (c) P(Z ≥ zo) = 0.4. Find zo. = 20 = (c) P(z0 ≤ Z ≤ 0.64) = 0.5988. Find zo. = (use two decimals)

In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.)   (a) Φ(c) = 0.9850     (b) P(0 ≤ Z ≤ c) = 0.2995     (c) P(c ≤ Z) = 0.1314     (d) P(−c ≤ Z ≤ c) = 0.6528     (e) P(c ≤ |Z|) = 0.0128     You may need to use the appropriate table in the Appendix of Tables to answer this question.

(i) Attempt the following questions. Show all necessary steps. Read the questions carefully. (ii) Any copied material from internet or your class fellows will get you ZERO marks. Q. 1 Let X be the number of bugs in the first draft of a piece of software, and let Y be the number of bugs remaining in the second draft of the same software. Their joint probability mass function is given by the following table: Y 0. 1 3 0. 0.03 0.14 0.09 0.08 1 0.05 0.10 K 0.04 0.04 0.09 0.08 0.09 (i) Obtain K so that it is the joint probability mass function; (ii) Find cumulative distribution function Fyy (x, y); (iii) Find the following probabilities using cdf obtained above (a) P(X 4), (c) P(X + Y > 3), (e) P(X < 3,Y < 2) 21

Let f(t) be the probability density function for the time it takes you to drive to school in the morning, where t is measured in minutes. Express "The probability that it takes you more than half an hour to get to school" as a probability.