1. If a variable can certain integer values between two given points is called ___________
a) Continuous random variable
b) Discrete random variable
c) Irregular random variable
d) Uncertain random variable
Explanation: This is the definition of a discrete random variable.
2. The expected value of a discrete random variable ‘x’ is given by ___________
a) P(x)
b) ∑ P(x)
c) ∑ x P(x)
d) 1
Explanation: ∑ x P(x)
3.If ‘X’ is a continuous random variable, then the expected value is given by ___________
a) P(X)
b) ∑ x P(x)
c) ∫ X P(X)
d) No value such as expected value
Explanation: Since X is a continuous random variable, its expected value is given by c.
4. Out of the following values, which one is not possible in probability?
a) P(x) = 1
b) ∑ x P(x) = 3
c) P(x) = 0.5
d) P(x) = – 0.5
Explanation: In probability P(x) is always greater than or equal to zero.
5. If E(x) = 2 and E(z) = 4, then E(z – x) =?
a) 2
b) 6
c) 0
d) Insufficient data
Explanation: E(z – x) = E(z) – E(x)
= 4 – 2 = 2.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.