Q1.A fair coin is tossed 10 times. What is the probability that only the first two tosses will yield heads?
Answer : Option CExplaination / Solution:
Number of elements in sample space is 210 Only one element "H,H,T,T,T,T,T,T,T,T, is event. Thus probability is 1/210
Q4.Consider two independent random variables X and Y with identical distributions. The variables X and Y take values 0, 1 and 2 with probabilities 1/2,1/4 and 1/4 respectively. What is the conditional probability P(X + Y = 2 X - Y = 0) ?
Sum of the principal diagonal element of matrix is equal to the sum of Eigen values. Sum of the diagonal element is -1 - 1 + 3 = 1.In only option (D), the sum of Eigen values is 1.
Q9.Consider the following statement about the linear dependence of the real valued functions y1 =
1, y2 = x and y3 = x2, over the field of real numbers.
I. y1, y2 and y3 are linearly independent on -1 ≤ x ≤ 0
II. y1, y2 and y3 are linearly dependent on 0 ≤ x ≤ 1
III. y1, y2 and y3 are linearly independent on 0 ≤ x ≤ 1
IV. y1, y2 and y3 are linearly dependent on -1 ≤ x ≤ 0