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Punjab (PTB) · Quarter book test · Free

1st Year Statistics 3rd Quarter Book Paper

40 marks · 1 hour · 28 questions. Covers: CHAP 7: Random Variables, CHAP 8: Probability Distributions, CHAP 9: Binomial and Hyper Geometric Probability Distribution.

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1st Year Statistics 3rd Quarter Book Paper

1st Year · Statistics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 40Time: 1 hour

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

  1. The random number o to 9 ae called random numbers:

    1. 1-digit

    2. 2-digit

    3. 3-digit

    4. 4-digit

  2. The number of trial in binomial distribution is:

    1. Not fixed

    2. Fixed

    3. Large

    4. Small

  3. If X and Y are independent random variables, then E(XY) is equal to

    1. E(XY)

    2. E(X) E(Y)

    3. XE(Y)

    4. YE(X)

  4. Probability proportional to size is abbreviated as:

    1. PPS

    2. SPP

    3. PPP

    4. PSP

  5. The parameters of the hypergeometric distribution h(x; N, n, k) are:

    1. x, N, k

    2. N, n, k

    3. x, n, k

    4. x, N, n, k

  6. If X and Y are independent random variables, then Var (X - Y) is equal to

    1. Var (X) - Var (Y)

    2. Var (X) + Var (Y)

    3. E(X - Y)2

    4. E(X + Y)2

  7. Random variable is also called:

    1. Discrete variabel

    2. Continuous variable

    3. Chance variable

    4. Variable

  8. In which distribution the successive trials are without replacement?

    1. Hypergeometric distribution

    2. Binomial distribution

    3. Continuous distribution

    4. None of these

  9. If the random variable X denotes the number of heads when three distinct coins are tossed, then X assumes the values

    1. 0, 1, 2, 3,

    2. 1, 3, 3, 1

    3. 1, 2, 3

    4. None of these

  10. PPS is used when we have information about:

    1. Random variables

    2. Probabillities

    3. Probability distribution

    4. Index numbers

  11. For a given binomial distribution with n fixed, if p < 0.5, then

    1. The binomial distribution will be skewed to the left

    2. The binomial distribution will be skewed to the right

    3. The binomial distribution will be symmetric

    4. None of these

  12. A discrete probability distribution may be represented by:

    1. A table

    2. A graph

    3. A mathematical equation

    4. All of these

Q2. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)

  1. Find the probability i.e., tossing a fair coin four times there will appear 1 tail and 3 heads.

  2. If  and = 0 elsewhere. Find P(X < 1.2).

  3. How random number can be generated?

  4. Is it possible to have a binomial distribution in the following case: P(X = -2)=0.1467

  5. If E(5X + 1) = 18 and E(5X + 10)2 = 530. Find Var(5X + 1).

  6. Make a random variable for number of heads when two coins are tossed.

  7. Define the binomial probability distribution.

  8. A random variable X has the following probability distribution.

    X -2 -1 0 1 2 3
    P(X) 0.1 K 0.2 2K 0.3 3K

    Find K.

  9. What is variable.

  10. Define the Binominal Probability Distribution.

  11. A continuous random variable X has a density function  for X = 2 to X = 4. Find P(X < 3.5)

  12. Make random variable for tail when three coins are tossed.

Q3. Long questions (Attempt any 3 of 4 · 3 × 4 = 12)

  1. Four randomly selected students from a class are asked their opinion about the teaching system as satisfactory (S) or not satisfactory (NS). Let Y denote the number of students saying satisfactory. Write down the possible outcomes and the possible Y values.

  2. The experience of a house-agent that he can provide suitable accommodation for 75 percent of the clients who come to him. If one a particular occasion 6 clients approach him independently, calculate the probability that at least 5 clients will bet satisfactory accommodation.

  3. There are three children in a family. Let the random variable denote the number of boys in a family. Write down the possible outcomes and the values assigned by the random variable assuming equal chances for boys and girls.

  4. Calculate Mean and Variance of the following probability distribution.

    x 0 1 2 3 4 5
    P(x) 0.1 0.2 0.3 0.2 0.1 0.1