1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. In random experiment, observations of random variable are classified as ___________
a) Events
b) Composition
c) Trials
d) Functions
Explanation: Events
8. The expectation of a random variable X(continuous or discrete) is given by _________
a) ∑xf(x), ∫xf(x)
b) ∑x2 f(x), ∫x2 f(x)
c) ∑f(x), ∫f(x)
d) ∑xf(x2), ∫xf(x2)
Explanation: The expectation of a random variable X is given by the summation (integral) of x times the function in its interval. If it is a continuous random variable, then summation is used and if it is discrete random variable, then integral is used.
9. Mean of a random variable X is given by _________
a) E(X)
b) E(X2)
c) E(X2) – (E(X))2
d) (E(X))2
Explanation: Mean is defined as the sum of the function in its domain multiplied with the random variable’s value. Hence mean is given by E(X) where X is a random variable.
10. Variance of a random variable X is given by _________
a) E(X)
b) E(X2)
c) E(X2) – (E(X))2
d) (E(X))2
Explanation: Variance of a random variable is nothing but the expectation of the square of the random variable subtracted by the expectation of X (mean of X) to the power 2. Therefore the variance is given by E(X2) – (E(X))2.