Probability and Statistics Questions and Answers – Probability Distributions – 2

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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

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

Answer: b
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

Answer: a
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

Answer: b
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

Answer: a
Explanation: The given statement is the definition of a continuous random variable.
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6. If Σ P(x) = k2 – 8 then, the value of k is?
a) 0
b) 1
c) 3
d) Insufficient data
View Answer

Answer: c
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

Answer: d
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

Answer: c
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

Answer: a
Explanation: Expected value and Mean are one and the same.
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10. The covariance of two independent random variable is ___________
a) 1
b) 0
c) – 1
d) Undefined
View Answer

Answer: b
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

Answer: a
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

Answer: a
Explanation: None.

Sanfoundry Global Education & Learning Series – Probability and Statistics.

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to practice all areas of Probability and Statistics Problems, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn