3. OQuestion Details To be fair, Pear entry tells the user the number of PearPho

Question

3. OQuestion Details To be fair, Pear entry tells the user the number of PearPhone 8 and PearPhone 8 Plus phones tha PearPhone 8 Plus phones the user may purchase. Let z -X+Y. The following is the joint probability mass 8 and PearPhone 8 Plus phones. The user selects an entry from a bin. The of new t he or she can purchase. Let x the number of PearPhone 8s and let Y the number of 107 321 107 x 1 .214 .214 0 2 .036 0 .001 a. What is the probability that Z-2 b. What is the probability X-1? c. What is the probability Y 0 d. Calculate the expected number of PearPhone 8 phones the user may purchase. e. Calculate the expected number of PearPhone 8 Plus phones the user may purchase. f. Calculate the expected value of z. g. Calculate the standard deviation of X h. Calculate the standard deviation of y i. What is the probability that X 2 given Y-0

Explanation / Answer

a) The required probability here is computed as;

P(Z = 2) = P(X = Y = 1) + P(X = 2, Y = 0) + P(X = 0, Y = 2) = 0.214 + 0.107 + 0.036 = 0.357

Therefore 0.357 is the required probability here

b) P(X = 1) is the sum of the second row computed as:

P(X = 1) = 0.214 + 0.214 + 0 = 0.428

Therefore 0.428 is the required probability here

c) P(Y = 0 ) is the sum of the first column computed as:

P(Y = 0) = 0.107 + 0.214 + 0.036 = 0.357

Therefore 0.357 is the required probability here

d) The marginal PMF for X here is given as:

P(X = 0) = 0.107 + 0.321 + 0.107 = 0.535
P(X = 1) = 0.428
P(X = 2) = 0.036 + 0.001 = 0.037

Therefore the expected number of Pearphone 8 phones the user may purchase here is computed as:

E(X) = 0 + 1*0.428 + 2*0.037 = 0.502

Therefore 0.502 is the expected value here.

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