Let X denote the number of Canon SLR cameras sold during a particular week by a certain store. The pmf of X is 1 2 3 4 0.1 0.2 0.3 0.25 0.15 Seventy percent of all customers who purchase these cameras also buy an extended warranty. Let Y denote the number of purchasers during this w A USE SALT (a) What is P(X = 4, Y = 2)? [Hint: This probability equals P(Y = 2|X = 4) - P(X = 4); now think of the four purchases as four trials of a bind PIY4 Ya ?) a 00518

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Let X denote the number of Canon SLR cameras sold during a particular week by a certain store. The pmf of X is
1
2
3
P(x)
0.3 0.25 0.15
0.1 0.2
Seventy percent of all customers who purchase these cameras also buy an extended warranty. Let Y denote the number of purchasers during this week who buy an extended warranty.
A USE SALT
(a) What is P(X = 4, Y = 2)? [Hint: This probability equals P(Y = 2|x = 4) - P(X = 4); now think of the four purchases as four trials of a binomial experiment, with success on a trial corresponding to buying an extended warranty.] (Round your answer to four decimal places.)
P(X = 4, Y= 2) = 0.0518
(b) Calculate P(X = Y). (Round your answer to four decimal places.)
P(X = Y) = 0.4014
(c) Determine the joint pmf of X and Y.
o ()(0.7)Y(0.7)*-Y - Pl)
o ()(0.7)"(0.7)*Y - P;6)
o ()(0.7)"(0.3)*-Y - Px,(x)
Determine the marginal pmf of Y. (Round your answers to four decimal places.)
y
1
2
P,V)
0.2480
0.3590
0.2678
0.1058
0.0194
You may need to use the appropriate table in the Appendix of Tables to answer this question.
Transcribed Image Text:Let X denote the number of Canon SLR cameras sold during a particular week by a certain store. The pmf of X is 1 2 3 P(x) 0.3 0.25 0.15 0.1 0.2 Seventy percent of all customers who purchase these cameras also buy an extended warranty. Let Y denote the number of purchasers during this week who buy an extended warranty. A USE SALT (a) What is P(X = 4, Y = 2)? [Hint: This probability equals P(Y = 2|x = 4) - P(X = 4); now think of the four purchases as four trials of a binomial experiment, with success on a trial corresponding to buying an extended warranty.] (Round your answer to four decimal places.) P(X = 4, Y= 2) = 0.0518 (b) Calculate P(X = Y). (Round your answer to four decimal places.) P(X = Y) = 0.4014 (c) Determine the joint pmf of X and Y. o ()(0.7)Y(0.7)*-Y - Pl) o ()(0.7)"(0.7)*Y - P;6) o ()(0.7)"(0.3)*-Y - Px,(x) Determine the marginal pmf of Y. (Round your answers to four decimal places.) y 1 2 P,V) 0.2480 0.3590 0.2678 0.1058 0.0194 You may need to use the appropriate table in the Appendix of Tables to answer this question.
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