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# Exercise 6.2: Mathematical Expectation

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Exercise 6.2

1. Find the expected value for the random variable of an unbiased die

2. Let X be a random variable defining number of students getting A grade. Find the expected value of X from the given table 3. The following table is describing about the probability mass function of the random variable X Find the standard deviation of x.

4. Let X be a continuous random variable with probability density function Find the expected value of X .

5. Let X be a continuous random variable with probability density function Find the mean and variance of X .

6. In an investment, a man can make a profit of 5,000 with a probability of 0.62 or a loss of 8,000 with a probability of 0 38 . Find the expected gain.

7. What are the properties of Mathematical expectation?

8. What do you understand by Mathematical expectation?

9. How do you define variance in terms of Mathematical expectation?

10. Define Mathematical expectation in terms of discrete random variable.

11. State the definition of Mathematical expectation using continuous random variable.

12. In a business venture a man can make a profit of 2,000 with a probability of 0.4 or have a loss of 1,000 with a probability of 0 6 . What is his expected, variance and standard deviation of profit?

13. The number of miles an automobile tire lasts before it reaches a critical point in tread wear can be represented by a p.d.f. Find the expected number of miles (in thousands) a tire would last until it reaches the critical tread wear point.

14. A person tosses a coin and is to receive 4 for a head and is to pay 2 for a tail. Find the expectation and variance of his gains.

15. Let X be a random variable and Y = 2X + 1. What is the variance of Y if variance of X is 5 ? 