Chapter Exam

Chapter 11: Probability Distributions — Online MCQ Test

Q: A random variable that can take only a finite or countable number of values is called a ______.

Answer: B. discrete random variable — A discrete random variable has a countable set of possible values. This is the standard definition used in probability distributions.

Q: For a probability mass function p(x), which condition must always be true?

Answer: C. The sum of all p(x) values is 1 — A probability mass function must satisfy the total probability condition. Hence, the sum of all probabilities is 1.

Q: If a random variable X takes values 0, 1, and 2 with probabilities 0.2, 0.5, and 0.3 respectively, then E(X) is

Answer: B. 1.1 — E(X) = Σxp(x) = 0×0.2 + 1×0.5 + 2×0.3 = 1.1. This is the weighted average of the values.

Q: A fair coin is tossed 4 times. If X denotes the number of heads, then the distribution of X is

Answer: B. Binomial with n = 4 and p = 1/2 — The number of heads in a fixed number of independent coin tosses follows a binomial distribution. Here n = 4 and p = 1/2.

Q: A Poisson distribution with parameter λ is used to approximate a binomial distribution when

Answer: B. n is large and p is small — The Poisson distribution is a good approximation to the binomial when the number of trials is large and the probability of success is small. In such cases, λ = np.

MATHS · CLASS 12th · Tamil Nadu State Board

Practice Chapter 11: Probability Distributions with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 12th MATHS. This chapter covers: Focusing on stochastic processes this chapter details discrete and continuous random variables probability mass and density functions. Students evaluate mathematical expectations m.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 11: Probability Distributions — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 12th MATHS — Chapter 11: Probability Distributions, with answers and explanations. These are sample questions; the exam has its own separate question set.

A random variable that can take only a finite or countable number of values is called a ______.

A. continuous random variable
B. discrete random variable ✓
C. mixed random variable
D. dependent random variable

Answer: B. discrete random variable
A discrete random variable has a countable set of possible values. This is the standard definition used in probability distributions.

For a probability mass function p(x), which condition must always be true?

A. p(x) can be negative for some values of x
B. The sum of all p(x) values is 0
C. The sum of all p(x) values is 1 ✓
D. p(x) must be greater than 1 for all x

Answer: C. The sum of all p(x) values is 1
A probability mass function must satisfy the total probability condition. Hence, the sum of all probabilities is 1.

If a random variable X takes values 0, 1, and 2 with probabilities 0.2, 0.5, and 0.3 respectively, then E(X) is

A. 0.9
B. 1.1 ✓
C. 1.3
D. 1.5

Answer: B. 1.1
E(X) = Σxp(x) = 0×0.2 + 1×0.5 + 2×0.3 = 1.1. This is the weighted average of the values.

A fair coin is tossed 4 times. If X denotes the number of heads, then the distribution of X is

A. Poisson with λ = 4
B. Binomial with n = 4 and p = 1/2 ✓
C. Normal with mean 2
D. Geometric with p = 1/2

Answer: B. Binomial with n = 4 and p = 1/2
The number of heads in a fixed number of independent coin tosses follows a binomial distribution. Here n = 4 and p = 1/2.

A Poisson distribution with parameter λ is used to approximate a binomial distribution when

A. n is small and p is large
B. n is large and p is small ✓
C. n = p
D. p = 1/2 always

Answer: B. n is large and p is small
The Poisson distribution is a good approximation to the binomial when the number of trials is large and the probability of success is small. In such cases, λ = np.