# Probability and Statistics Questions and Answers – Probability Distributions – 2

«
»

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

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

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

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

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

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

6. If Σ P(x) = k2 – 8 then, the value of k is?
a) 0
b) 1
c) 3
d) Insufficient data

Explanation: Σ P(x) = k2 – 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

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

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

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

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

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 