7- A certain market has both an express checkout line and a superexpress checkout line. Let $X_1$ denote the number of customers in line at the express checkout at a particular time of day, and let $X_2$ denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of $X_1$ and $X_2$ is as given in the accompanying table. egin{tabular}{cc|cccc} & & & $x_2$ & & \ & & 0 & 1 & 2 & 3 \ hline & 0 & .08 & .07 & .04 & .00 \ & 1 & .06 & .15 & .05 & .04 \ $x_1$ & 2 & .05 & .04 & .10 & .06 \ & 3 & .00 & .03 & .04 & .07 \ & 4 & .00 & .01 & .05 & .06 \ end{tabular} a. What is $P(X_1 = 1, X_2 = 1)$, that is, the probability that there is exactly one customer in each line? b. What is $P(X_1 = X_2)$, that is, the probability that the numbers of customers in the two lines are identical? c. Let $A$ denote the event that there are at least two more customers in one line than in the other line. Express $A$ in terms of $X_1$ and $X_2$, and calculate the probability of this event. d. What is the probability that the total number of customers in the two lines is exactly four? At least four?
Added by Vicenta B.
Close
Your feedback will help us improve your experience
Sri K and 57 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Sri K.
A certain market has both an express checkout line and a superexpress checkout line. Let X1 denote the number of customers in line at the express checkout at a particular time of day, and let X2 denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X1 and X2 is as given in the accompanying table. x2 0 1 2 3 x1 0 0.09 0.06 0.04 0.00 1 0.05 0.15 0.05 0.04 2 0.05 0.04 0.10 0.06 3 0.00 0.04 0.04 0.07 4 0.00 0.02 0.05 0.05 (a) What is P(X1 = 1, X2 = 1), that is, the probability that there is exactly one customer in each line? P(X1 = 1, X2 = 1) = (b) What is P(X1 = X2), that is, the probability that the numbers of customers in the two lines are identical? P(X1 = X2) = (c) Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X1 and X2. A = {X1 ≤ 2 + X2 ∪ X2 ≥ 2 + X1} A = {X1 ≥ 2 + X2 ∪ X2 ≤ 2 + X1} A = {X1 ≥ 2 + X2 ∪ X2 ≥ 2 + X1} A = {X1 ≤ 2 + X2 ∪ X2 ≤ 2 + X1} Calculate the probability of this event. P(A) = (d) What is the probability that the total number of customers in the two lines is exactly four? At least four? P(exactly four) = P(at least four) =
Samriddhi S.
Certain market has both an express checkout line and a superexpress checkout line. Let X1 denote the number of customers in the express checkout line at a particular time, and let X2 denote the number of customers in the superexpress checkout line at the same time. Suppose the joint pmf of X1 and X2 is given by the accompanying table: (a) What is P(X1 = 1, X2 = 1), that is, the probability that there is exactly one customer in each line? (b) What is P(X1 = X2), that is, the probability that the numbers of customers in the two lines are identical? (c) Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X1 and X2. Calculate the probability of this event P(A). (d) What is the probability that the total number of customers in the two lines is exactly four? At least four?
Madhur L.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD