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
View Answer
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) = k2 – 8 then, the value of k is?
a) 0
b) 1
c) 3
d) Insufficient data
View Answer
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
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.
to practice all areas of Probability and Statistics Problems, here is complete set of 1000+ Multiple Choice Questions and Answers.
Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!