Let X and Y be two discrete random variables with a joint probability distributi
ID: 2946998 • Letter: L
Question
Let X and Y be two discrete random variables with a joint probability distribution described in the following table: Rain (X-0) No rain (X-1) Total Long commute (WO) 0.05 0.20 0.25 Short commute 0.50 0.25 10.75 (Y-1) Total 0.55 0.45 1.00 a) [6 ptsjExplain the meaning of the number in row 4 column 2, the number "0.55" b) [8 pts Suppose W-2+3X, what is the expected value of W (Hint, you need to find E(X) first) c) [6 pts] Conditional on raining tomorrow, what is the probability that having short commute (Round up to two decimal points)?Explanation / Answer
a)
0.55 is the probability of rain
b)
P(X = 0) = 0.55
P(X = 1) = 0.45
E(X) = 0*0.55 + 1 * 0.45 = 0.45
W = 2+ 3 X
E(W) = 2 + 3 E(X)
= 2 + 3 *0.45
= 3.35
c)
P(short commute|rain tomorrow)
= P(short commute and rain tomorrow)/P(rain tomorrow)
= 0.5/0.55
=10/11
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.