Probability and Statistics Mid - I, September - 2014

1.The mean of uniform probability distribution f(x) = 1/n for x = 1,2,3…..n is
  • n
  • n2
  • (n-1)/2
  • (n+1)/2
Answer: A
2.If a r.v takes atmost a countable number of values, it is called a _______r.v
  • Continuous
  • Discrete
  • Standard deviation
  • none
Answer: B
3.xk P(X=x) =
  • E(kx)
  • E(xk)
  • xk E(X)
  • xE(xk)
Answer: B
4.If X is a normal variate then mean deviation about the mean μ is
  • /2
  • (3/4)
  • (4/5)
Answer: D
5.The regression coefficient is independent of ______
  • Origin
  • Scale
  • Both A&B
  • None
Answer: A
6.The graph of normal distribution is symmetric with respect to the line ____
  • x =
  • x =
  • x = z
  • Anti symmetric
Answer: A
7.The joint probability density function of random variables X, Y is f(x, y) = e -(x + y); x ≥ 0,y ≥ 0 the conditional probability density function of X on Y is _______
  • e-y
  • e-x
  • ex
  • e-(x+y)
Answer: B
8.The given two regression lines are x + 2y - 5 = 0 and 2x + 3y - 8 = 0, mean of x and y is
  • (1, 3)
  • (2, 1)
  • (3, 2)
  • (1, 2)
Answer: D
9.If the size of the sample is 5 and size of the population is 2000. The corrector factor is
  • 0.99
  • 9.99
  • 99.9
  • None
Answer: A
10.A population consisting of all real number is _____
  • Infinte population
  • finite population
  • sample
  • None
Answer: A
11.The nth moment about the mean μ of distribution is expectation of _______________
Answer: [(x - )n]
12.The moment generating function of a random variable x with pdf f(x) = e-x for x ≥ 0. the second moment about the origin___________
Answer: 2
13.A finite subset of statistical individuals in a population is ________
Answer: sample
14.The probable error of the correlation coefficient ____________
Answer: 0.6745 * S.E
15.Moment generating function of Binomial distribution is__________
Answer: (q + pet)n
16.If X and Y are two independent random variable, a and b are constant then V(aX - bY) = ______
Answer: a2var(X) + b2Var(Y)
17.The geometrical mean of two regression coefficient is_________
Answer: Correlation coefficient
18.If x is Poisson variate such that P(X = k) = P(X = k + 1) for some positive integer K them mean =___
Answer: k + 1
19.Let X and Y are two Random variables having the joint probability density function fX,Y(x, y) is stochastically independent if_______
Answer: fX,Y(x,y)= fX(x) . fY(y)
20.When two dice are thrown, the expectation for sum 7 is _______
Answer: 7/6