This set of Probability and Statistics Problems focuses on “Probability Distributions – 2”.

1. If the values taken by a random variable are negative, the negative values will have ___________

a) Positive probability

b) Negative Probability

c) May have negative or positive probabilities

d) Insufficient data

View Answer

Explanation: Probabilities are always positive and not greater than 1.

2. If f(x) is a probability density function of a continuous random variable, then \(\int_{-∞}^∞\)f(x)=?

a) 0

b) 1

c) undefined

d) Insufficient data

View Answer

Explanation: Sum of all probabilities of a sample space is always 1.

3. The variable that assigns a real number value to an event in a sample space is called ___________

a) Random variable

b) Defined variable

c) Uncertain variable

d) Static variable

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Explanation: The above given statement is the definition of a random variable.

4. A random variable that assumes a finite or a countably infinite number of values is called ___________

a) Continuous random variable

b) Discrete random variable

c) Irregular random variable

d) Uncertain random variable

View Answer

Explanation: The given statement is the definition of a discrete random variable.

5. A random variable that assume a infinite or a uncountably infinite number of values is called ___________

a) Continuous random variable

b) Discrete random variable

c) Irregular random variable

d) Uncertain random variable

View Answer

Explanation: The given statement is the definition of a continuous random variable.

6. If Σ P(x) = k^{2} – 8 then, the value of k is?

a) 0

b) 1

c) 3

d) Insufficient data

View Answer

Explanation: Σ P(x) = k

^{2}– 8 = 1

On solving, we get k = 3.

7. If P(x) = 0.5 and x = 4, then E(x) = ?

a) 1

b) 0.5

c) 4

d) 2

View Answer

Explanation: E(x) = x P(x) = 0.5 * 4 = 2.

8. In a discrete probability distribution, the sum of all probabilities is always?

a) 0

b) Infinite

c) 1

d) Undefined

View Answer

Explanation: It is based on the basic axiom of probability distribution.

9. The expected value of a random variable is its ___________

a) Mean

b) Standard Deviation

c) Mean Deviation

d) Variance

View Answer

Explanation: Expected value and Mean are one and the same.

10. The covariance of two independent random variable is ___________

a) 1

b) 0

c) – 1

d) Undefined

View Answer

Explanation: Two random variables are said to be independent if their covariance is zero.

11. The weight of persons in a state is a ___________

a) Continuous random variable

b) Discrete random variable

c) Irregular random variable

d) Not a random variable

View Answer

Explanation: Since the distribution is continuous, its a continuous random variable.

12. In random experiment, observations of random variable are classified as ___________

a) Events

b) Composition

c) Trials

d) Functions

View Answer

Explanation: None.

**Sanfoundry Global Education & Learning Series – Probability and Statistics.**

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