Solapur University Question Paper
B.Com. – III (Sem. – VI) Examination, 2014
ADVANCED STATISTICS (Paper – I)
Day and Date : Wednesday, 2-4-2014
Max. Marks : 50
Time : 11.00 a.m. to 1.00 p.m.
N.B. : 1) All questions are compulsory.
2) Each question carries equal marks.
3) Graph papers will be supplied on request.
4) Use of soundless calculator is allowed.
1. Choose the correct alternative : 10
1) If X is a random variable with probability distribution {x, P(x)}, then ∑xP(x) is called
a) mean of X b) variance of X c) both a) and b) d) none of these
2) Var (X + constant) is equal to
a) Var (X) b) Var (constant) c) Var (X) + constant d) None of these
3) If a and b are constants, then E (aX + b) =
a) a E(X) b) E (X) c) aE(X) + b d) none of these
4) Mean of binomial distribution is equal to
a) pq b) np c) npq d) none of these
5) In binomial distribution ‘p’ denotes probability of
a) success b) failure c) both a) and b) d) none of these
6. For the binomial distribution ; if n = 4 and 3 1 p = , then the value of variance is
a) 8/3 b) 8/9 c) 4/3 d) none of these
7) Mean is equal to variance in case of
a) Binomial distribution b) Poisson distribution c) Normal distribution d) None of these
8) If either p or q is very small, but n is sufficiently large, the binomial distribution is very closly approximated by
a) Poisson distribution b) Normal distribution c) Geometric distribution d) None of these
9) If X ~ N ( , ) 2 μ σ variate, then mean of X is
a) μ b) 2μ c) 1 d) none of these
10) Normal probability curve is
a) symmetric b) bell shaped c) both a) and b) d) none of these
2. a) Define binomial distribution. If mean and variance of binomial distribution are 20 and 16 respectively. Find its parameters n and p.
5 b) Let X denote the number of heads obtained in a random toss of three coins. The Prob. distribution of X is X : 0 1 2 3 P(x) : 8 1 8 3 8 3 8 1 Find : i) E (X) and ii) E (2X + 1). 5
3. a) If X and Y are independent r.v’s then show that E (XY) = E (X) . E(Y).
5 b) A discrete r.v.X has Poisson distribution such that P(X = 2) = P(X = 3) Find P (X = 4). (Given e–3 = 0.0498).
4. Attempt any one of the following : 10 a) State probability mass function of Poisson distribution. Give the situations where Poisson distribution is applicable. b) For a normal variate X with mean = 25 and SD = 10. Find the area between : i) X = 25 to X = 35 and ii) X ≥ 15 (Given that area under normal curve z = 0 to z = 1 is 0.3413). 5. Attempt any one of the following : 10 a) Define normal distribution . State the properties of normal distribution. b) The joint probability distribution of (X, Y) is Y –1 0 1 X –1 0.0 0.2 0.0 0 0.1 0.2 0.1 1 0.1 0.2 0.1 Find : i) E (X/Y = –1) and ii) V (X/Y = –1). _____________________
B.Com. – III (Sem. – VI) Examination, 2014
ADVANCED STATISTICS (Paper – I)
Day and Date : Wednesday, 2-4-2014
Max. Marks : 50
Time : 11.00 a.m. to 1.00 p.m.
N.B. : 1) All questions are compulsory.
2) Each question carries equal marks.
3) Graph papers will be supplied on request.
4) Use of soundless calculator is allowed.
1. Choose the correct alternative : 10
1) If X is a random variable with probability distribution {x, P(x)}, then ∑xP(x) is called
a) mean of X b) variance of X c) both a) and b) d) none of these
2) Var (X + constant) is equal to
a) Var (X) b) Var (constant) c) Var (X) + constant d) None of these
3) If a and b are constants, then E (aX + b) =
a) a E(X) b) E (X) c) aE(X) + b d) none of these
4) Mean of binomial distribution is equal to
a) pq b) np c) npq d) none of these
5) In binomial distribution ‘p’ denotes probability of
a) success b) failure c) both a) and b) d) none of these
6. For the binomial distribution ; if n = 4 and 3 1 p = , then the value of variance is
a) 8/3 b) 8/9 c) 4/3 d) none of these
7) Mean is equal to variance in case of
a) Binomial distribution b) Poisson distribution c) Normal distribution d) None of these
8) If either p or q is very small, but n is sufficiently large, the binomial distribution is very closly approximated by
a) Poisson distribution b) Normal distribution c) Geometric distribution d) None of these
9) If X ~ N ( , ) 2 μ σ variate, then mean of X is
a) μ b) 2μ c) 1 d) none of these
10) Normal probability curve is
a) symmetric b) bell shaped c) both a) and b) d) none of these
2. a) Define binomial distribution. If mean and variance of binomial distribution are 20 and 16 respectively. Find its parameters n and p.
5 b) Let X denote the number of heads obtained in a random toss of three coins. The Prob. distribution of X is X : 0 1 2 3 P(x) : 8 1 8 3 8 3 8 1 Find : i) E (X) and ii) E (2X + 1). 5
3. a) If X and Y are independent r.v’s then show that E (XY) = E (X) . E(Y).
5 b) A discrete r.v.X has Poisson distribution such that P(X = 2) = P(X = 3) Find P (X = 4). (Given e–3 = 0.0498).
4. Attempt any one of the following : 10 a) State probability mass function of Poisson distribution. Give the situations where Poisson distribution is applicable. b) For a normal variate X with mean = 25 and SD = 10. Find the area between : i) X = 25 to X = 35 and ii) X ≥ 15 (Given that area under normal curve z = 0 to z = 1 is 0.3413). 5. Attempt any one of the following : 10 a) Define normal distribution . State the properties of normal distribution. b) The joint probability distribution of (X, Y) is Y –1 0 1 X –1 0.0 0.2 0.0 0 0.1 0.2 0.1 1 0.1 0.2 0.1 Find : i) E (X/Y = –1) and ii) V (X/Y = –1). _____________________
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