Probability Theory and Stochastic Processes Mid - I, September - 2014

1.Two - dimensional product space is known as
  • vector
  • Range of sample space
  • sample space
  • Phasor
Answer: B
2.A real RV is defined as
  • A real function of the elements of a sample space
  • A discrete function of the elements
  • A continuous function of the elements
  • A continuous function of the elements of a sample space
Answer: A
3.If a continuous random variable X has the probability density function  and the Mean of the X is 3/9, then the variance is
  • 3/320
  • 11/320
  • 21/320
  • 19/320
Answer: D
4.The distribution function of one random variable X conditioned by a second random variable Y With interval { ya ≤ y ≤ yb } is known as
  • Moment generation
  • point conditioning
  • expectation
  • interval conditioning
Answer: D
5.Central limiting theorem is mostly applicable to statistically
  • Dependent RV
  • independent RV
  • all RV
  • any RV
Answer: B
6.Let A be any event defined on a sample space, then P(A) IS
  • ≥ 0
  • < 
  • > 
  • ≥ 1
Answer: A
7.For n = 1, 2,…N    P(Bn / A) =
  • P (An/Bn).P (Bn)/P (A/Bn).p(B1) + …….. + P(B)
  • P (Bn/A) .P (A)/ P (A/B1) .P (B2) +…….+P(A). P(B)
  • P (A/Bn).P (An)/P (A/B1). P (B1) + ……+P (A/B). P(B)
  • P (A/Bn).P(Bn)/P (A/B1) .P (B1)+…..+P(A/Bn).P(Bn)
Answer: D
8.The exponential density function is defined as
  • e (-(x-a)/b)     for   x < a
  • 1/b    for x > a
  • 1/b e (-(x-a)/b)    for x > a
  • 1/b e (-(x-a)/b)    for x < a
Answer: C
9.The normalized third central moment is known as
  • Mean function
  • Skewness of the density function
  • Standard Deviation
  • Variance of the density function
Answer: B
10.If X is a RV with event A , then  
  • 1
  • 0
  • -1
Answer: A
11.The probability of events {X =  } and {x = -  } are ______________
Answer: Zero
12.The events in the combined sample space are considered as______________
Answer: pair of events
13.The relation between conditional probabilities P (A/B) and P (B/A) is derived by using _________ theorem
Answer: Baye’s
14.The uniform probability density function in the range { a, b } can be expressed as ____________
Answer: 1 / (b − a)
15.Given that P (A) = 0.75, P(B) = 0.5, P(A B) = 0.45 then P(AUB) = _____________
Answer: 0.8
16.The nth central moment, μn =_________________
Answer:
17.If the probability density function of a random variable X is 1/2 sinx in 0 ≤ x ≤ , then the variance is _________________
Answer:
18.The variance of the random variable, taking values of getting heads if two coins are tossed is __________
Answer: ½
19.The marginal Distribution function is fX,Y(x, ) = _____________ and fX,Y( , y) = ___________
Answer: FX(x), FY(y)
20.The characteristic function and __________________ are the methods used for finding the moments.
Answer: moment generating function