Probability Theory and Stochastic Processes Mid - I, September - 2011

1.A die is thrown 256 times. An even digit turns up 150 times. Then the die is
  • Biased
  • Un biased
  • not determined
  • none
Answer: B
2.If n=40, Error is 0.5, σ = 1.6 minutes then Z(α/2) is
  • 1.86
  • 1.96
  • 2.76
  • 2.86
Answer: B
3.A population consisting of all Integers is an example of
  • Finite
  • Infinite
  • sample
  • None
Answer: B
4.The Probability distribution of a statistic is called
  • Normal
  • Binomial
  • Poisson
  • Sampling
Answer: D
5.In a city 250 men out of 750 men were found to be drunkers. Then │z │
  • 2.25
  • 2.5
  • 5.25
  • 5.50
Answer: C
6.Variance of Poisson distribution V(x) is
  • E(x)
  • E(x)^2
  • E(x^2) – [E(x)]^2
  • None
Answer: C
7.The Probability distribution of a Statistic is called
  • Normal distribution
  • sampling distribution
  • Binomial distribution
  • Poisson distribution
Answer: B
8.The Probability that a leap year will have 53 Mondays is
  • 4/7
  • 3/7
  • 2/7
  • 1/7
Answer: C
9.If a coin is tossed 6 times in Succession, the Probability of getting at least one tail is
  • 62/63
  • 63/64
  • 6/32
  • 1/64
Answer: B
10.The standard error of the statistic sample mean is
  • σ/sqrt(π)
  • σ^2/sqrt(π)
  • sqrt(σ/π)
  • None
Answer: A
11.If X and Y are independent random variables, then E(XY) = __________
Answer: E(X).E(Y)
12.The totality of Observation is called ________________
Answer: Population
13.For Continuous Probability distribution variance is _______________
Answer: σ^2 =-α ∫ +α (x-µ) (x-µ) f(x)dx
14.If S is a sample space, E1,E2 are any events is S then P(E1) = _____________
Answer: P(E1) + P(E2) – P(E12)
15.The probability of getting 2 Tails in tossing 5 coins is _____________
Answer: 5/256
16.P (A/B) = ____________________
Answer: P(A n B)/P(B)
17.The Mean of the density function f(x) = is _________________
Answer: 1/ƛ
18.Standardized random variable z = ___________
Answer: (x-µ)/ σ
19.If P(A^c) = 3/8 , P(B^c) = 1/2 , P(AnB) = 1/4 then P(B/A) value is __________
Answer: 0.4
20.By Baye’s Theorem P(E1/E2) = _____________
Answer: P(E1).P(E2/E1)/(P(E1)P(E2/E1)+P(E1')P(E2/E1'))