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Punjab (PTB) · Chapter test · Free

1st Year Statistics Chapter 8 TestProbability Distributions

30 marks · 40 minutes · 21 questions. Covers: CHAP 8: Probability Distributions.

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1st Year Statistics Chapter 8 Test

1st Year · Statistics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 30Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  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. 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

  3. 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

  4. A discrete probability distribution may be represented by:

    1. A table

    2. A graph

    3. A mathematical equation

    4. All of these

  5. If X and Y are independent random variables, then S.D. (X - Y) is equal to

    3. S.D.(X) + S.D.(Y)

    4. S.D.(X) - S.D.(Y)

  6. A continuous probability distribution may be represented by:

    1. A table

    2. A graph

    3. A mathematical equation

    4. Both (b) and (c)

  7. Probability density function is the probability function of ...... random variable:

    1. Continuous

    2. Discrete

    3. Qualitative

    4. None

  8. If , where 'a' and 'b' are any two constants the Var(y)=

    1. a Var(X) + b

    2. Var(X) + b

    3. a2 Var(X)

    4. a Var(X)

  9. If X is a random variable and a and b are constants, then Var (a + bX) is equal to

    1. Var (a) + Var (bX)

    2. Var (a) + b Var (X)

    3. b2 Var (X)

    4. b Var (X)

  10. If X and Y are random variables, then E(X - Y) is equal to

    1. E(X) + E(Y)

    2. E(X) - E(Y)

    3. X - E(Y)

    4. E(X) - Y

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

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

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

  3. 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.

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

  5. A continuous random variable X has probability density function giving f(x) = cx for 0 < X < 2. Find probability that X < 1.5.

  6. A continuous random variable X which can assume values between X = 2 and X = 8 inclusive has a density function given by a(x+30), where 'a' is a constant. Find .

  7. Which of the following functions f(x) is a valid probability function? f(x) = (x + 1)/8,

  8. A continuous random variable X has a density function  for X = 2 to X = 4. Find P(X = 1.5).

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  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. 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

  3. Determine the value of c so that the function can serve as a probability function of a random variable. cy for Y = 1,2,3,4,5