Not sure if my answers that are written are correct. I need help with the entire

Question

Not sure if my answers that are written are correct. I need help with the entire question. 3. Question Details My Notes Ask Your Teacher To be fair, Pear Computer Company is holding a lottery for prospective purchasers of new PearPhone 8 and PearPhone 8 Plus phones. The user selects an entry from a bin. The entry tells the user the number of PearPhone 8 and PearPhone 8 Plus phones that he or she can purchase. Let X = the number of PearPhone 8s and let Y = the number of PearPhone 8 Plus phones the user may purchase. Let Z- X+Y. The following is the joint probability mass function for X and Y: 107.321 214.214 036 0 107 X 1 001 a. What is the probability that Z = 2? b. What is the probability X -1? 0428 C. What is the probability Y = 0? (0357D d. Calculate the expected number of PearPhone 8 phones the user may purchase. 3.95 e. Calculate the expected number of PearPhone 8 Plus phones the user may purchase. 1.84 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? Add any comments below

Explanation / Answer

from above below is joint probability:

below is marginal distribution of X:

and marginal distribution of Y:

a)P(Z=2)=P(X=0,Y=2)+P(X=1,Y=1 )+P(X=2,Y=0)=0.107+0.214+0.036 =0.3570

b)P(X=1)=0.4280

c) P(Y=0)=0.3570

d)E(X)=0.5020

e)E(Y)=0.7510

f)E(Z)=E(X)+E(Y)=1.2530

g)SD(X)=(0.3240)1/2 =0.5692

h) SD(Y)=(0.4030)1/2 =0.6348

i) P(X=2|Y=0)=0.036/0.3570=0.1008

y x 0 1 2 Total 0 0.1070 0.3210 0.1070 0.5350 1 0.2140 0.2140 0.0000 0.4280 2 0.0360 0.0000 0.0010 0.0370 Total 0.3570 0.5350 0.1080 1.0000

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