Probability and Statistics Problems 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
Answer: a
Clarification: 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
Answer: b
Clarification: 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
Answer: a
Clarification: 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
Answer: b
Clarification: 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
Answer: a
Clarification: 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
Answer: c
Clarification: 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
Answer: d
Clarification: 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
Answer: c
Clarification: 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
Answer: a
Clarification: 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
Answer: b
Clarification: 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
Answer: a
Clarification: 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
Answer: a
Clarification: None.