Let X denote the number of Canon digital cameras sold during

Let X denote the number of Canon digital cameras sold during a particular week by a certain store.
The probability function for X is given by:
x 0 1 2 3 4
P(X=x) 0.1 0.2 0.3 0.25 0.15

Additionally, sixty 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. What is the probability that four cameras are sold during one week and two extended warranties are
purchased?
b. Construct a table that contains the joint distribution of X and Y.
c. Find the conditional distribution of Y, given that 3 cameras are sold.
d. What is the expected number of extended warranties bought, given that 3 cameras are sold?

Solution

x: Number of Canon digital cameras sold during a particular week

y: no of camera sold with extended warranty , sixty percent of all customers.

there probability is as follows

y:                   0             1             2           3               4

p(Y=y)           0.06       0.12      0.18       0.15          0.09

(b) their joint probability table is as follow;

    (a)

Pr(X=4, y=2) = 0.027

(c)      y :                          0                 1                2                  3                          4

       pr(Y=y/X=3)            0.015           0.030        0.045            0.0375               0.0225