Book back answers and solution for Exercise questions - Maths: Mathematical Expectation: Exercise Problems with Answer, Solution

**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* = 2*X* + 1. What is the variance of *Y* if variance of *X *is 5 ?

**Answers:**

Tags : Problem Questions with Answer, Solution , 12th Business Maths and Statistics : Chapter 6 : Random Variable and Mathematical Expectation

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12th Business Maths and Statistics : Chapter 6 : Random Variable and Mathematical Expectation : Exercise 6.2: Mathematical Expectation | Problem Questions with Answer, Solution

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