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Punjab (PTB) · Half book test · Free

1st Year Statistics Second half Book Paper

50 marks · 1 hour 30 minutes · 35 questions. Covers: 4 chapters (CHAP 6: Probability to CHAP 9: Binomial and Hyper Geometric Probability Distribution).

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1st Year Statistics Second half Book Paper

1st Year · Statistics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 50Time: 1 hour 30 minutes

Q1. Multiple choice questions (Attempt all · 15 × 1 = 15)

  1. 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)

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

    1. 1-digit

    2. 2-digit

    3. 3-digit

    4. 4-digit

  3. The number of trial in binomial distribution is:

    1. Not fixed

    2. Fixed

    3. Large

    4. Small

  4. The probability of drawing a king of spade from a pack of 52 cards is

  5. 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

  6. Probability proportional to size is abbreviated as:

    1. PPS

    2. SPP

    3. PPP

    4. PSP

  7. 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

  8. When a pair of dice is rolled, the sum of uppermost dots vary from:

    1. 0 to 10

    2. 1 to 11

    3. 2 to 19

    4. 2 to 12

  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. Random variable is also called:

    1. Discrete variabel

    2. Continuous variable

    3. Chance variable

    4. Variable

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

    1. Hypergeometric distribution

    2. Binomial distribution

    3. Continuous distribution

    4. None of these

  12. If , then A and B are

    1. Mutually exclusive

    2. Independent

    3. Not mutually exclusive

    4. None of these

  13. A discrete probability distribution may be represented by:

    1. A table

    2. A graph

    3. A mathematical equation

    4. All of these

  14. PPS is used when we have information about:

    1. Random variables

    2. Probabillities

    3. Probability distribution

    4. Index numbers

  15. 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

Q2. Short questions (Attempt any 10 of 15 · 10 × 2 = 20)

  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. What is the sample space when three distinct coins are tossed simultaneously? Also specify the event A 'exactly two heads occur'.

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

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

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

  8. Solve: 

  9. Define the binomial probability distribution.

  10. 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.

  11. What is variable.

  12. Evaluate the following: 

  13. Define the Binominal Probability Distribution.

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

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

Q3. Long questions (Attempt any 3 of 5 · 3 × 5 = 15)

  1. 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.

  2. For two independent events A and B, P(A) = 0.25 and P(B) = 0.40. Find ?

  3. 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.

  4. 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.

  5. Generate the first 6 random digits using the pseudo-random number generator with m=100, a=21, b=7, xo=10.