# A supermarket has two customers waiting for their purchases at counter 1 and one customer waiting to pay at counter 2: Probability & Mathematical Statistics Assignment, UTAR, Malaysia

School

###### Universiti Teknologi Malaysia (UTM)Universiti Tunku Abdul Rahman (UTAR)

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Assignment Type

Subject

Date

###### 29/01/2022
• QUESTION 1
A supermarket has two customers waiting for their purchases at counter 1 and one customer waiting to pay at counter 2. Let X1 and X2 denote the numbers of customers who spend more than RM50 on groceries at the respective counter. Suppose that X1 and X2 are independent binomial random variables, with the probability that a customer at the counter I will spend more than RM50 equal to 0.2 and the probability that a customer at counter 2 will spend more than RM50 equal to 0.3.
1. State the joint probability mass function (pmf) of X1 and X2 based on the case study.
2. Find the joint pmf of X1 and X2 in tabular form.
3. Find the marginal distribution of X1 and X2 in tabular form.
4. The probability that not more than one of the three customers will spend more than RM50.
5. Determine the mean and variance of W = 3X1 − 2X2 + 5

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