## 1. Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is 0.6. If she studies mathematics on a day, then the, probability that she studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?

## 2. A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?

## 3. A machine produces 0, 1 or 2 defective pieces in a day with associated probability of $$\frac{1}{6},\,\frac{2}{3}$$ and $$\frac{1}{6}$$ respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are

## 4. Let X and Y be two independent random variables. Which one of the relations between expectation (E), variance (Var) and covariance (Cov) given below is FALSE?

## 5. The box 1 contains chips numbered 3, 6, 9, 12 and 15. The box 2 contains chips numbered 6, 11, 16, 21 and 26. Two chips, one from each box, are drawn at random. The numbers written on these chips are multiplied. The probability for the product to be an even number is

## 6. For random variable x($$ - \infty $$ < x < $$\infty $$) following normal distribution, the mean is μ = 100. If probability is P = α for x ≥ 110. Then probability of x lying between 90 and 110 i.e., P(90 ≤ x ≤ 110) is equal to

## 7. A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red is

## 8. In the following table, x is a discrete random variable and p(x) is the probability density. The standard deviation of x is

x
1
2
3
p(x)
0.3
0.6
0.1

x | 1 | 2 | 3 |

p(x) | 0.3 | 0.6 | 0.1 |

## 9. Three companies X, Y and Z supply computers to a university. The percentage of computers supplied by them and the probability of those being defective are tabulated below:

Company
% of computer
Probability of being supplied defective
X
60%
0.01
Y
30%
0.02
Z
10%
0.03

Given that a computer is defective, the probability that it was supplied by Y is

Company | % of computer | Probability of being supplied defective |

X | 60% | 0.01 |

Y | 30% | 0.02 |

Z | 10% | 0.03 |

Given that a computer is defective, the probability that it was supplied by Y is

## 10. Let X_{1} and X_{2} be two independent exponentially distributed random variables with means 0.5 and 0.25 respectively. Then Y = min (X_{1}, X_{2}) is

_{1}and X

_{2}be two independent exponentially distributed random variables with means 0.5 and 0.25 respectively. Then Y = min (X

_{1}, X

_{2}) is

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