Maths Book back answers and solution for Exercise questions - Mathematics : Probability Distributions: Mathematical Expectation - Exercise Problem Questions with Answer, Solution

**EXERCISE 11.4**

**1. For the random variable X with the given probability mass function as below, find the mean and variance.**

**2. Two balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X.**

**3. If μ and σ 2 are the mean and variance of the discrete random variable X , and E ( X + 3) = 10 and E ( X + 3)2 = 116 , find μ and σ 2.**

**4. Four fair coins are tossed once. Find the probability mass function, mean and variance for number of heads occurred.**

**5. A commuter train arrives punctually at a station every half hour. Each morning, a student leaves his house to the train station. Let X denote the amount of time, in minutes, that the student waits for the train from the time he reaches the train station. It is known that the pdf of X is**

**Obtain and interpret the expected value of the random variable X .**

**6. The time to failure in thousands of hours of an electronic equipment used in a manufactured computer has the density function**

**Find the expected life of this electronic equipment.**

**7. The probability density function of the random variable X is given by**

**find the mean and variance of X .**

**8. A lottery with 600 tickets gives one prize of ₹200, four prizes of ₹100, and six prizes of ₹ 50. If the ticket costs is ₹ 2, find the expected winning amount of a ticket.**

**(1) (i) 2.3 , 2.81 (ii) 1.67 , 0.56 (iii) 5/3 , 1/18 (iv) 2,4**

**(2) **

**(3) **

**(5) 15 minutes (6) 1/3 (7) 1/2 , 1/8 (8) Loss ₹. 0.50**

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12th Maths : UNIT 11 : Probability Distributions : Exercise 11.4: Mathematical Expectation | Problem Questions with Answer, Solution

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