Probability

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Question 1

Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time. What is the probability that the sum total of values that turn up is at least 6?

  • A

    10/21

  • B

    5/12

  • C

    2/3

  • D

    1/6

Question 2

Consider a random variable X that takes values +1 and −1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = −1 and +1 are

  • A

    0 and 0.5

  • B

    0 and 1

  • C

    0.5 and 1

  • D

    0.25 and 0.75

Question 3

Consider a link with packet loss probability of 0.2. What is the expected number of transmissions it would take to transfer 200 packets given that the stop and wait protocol is used?

  • A

    125

  • B

    250

  • C

    225

  • D

    150

Question 4

A class of 24 students occupies a classroom containing 4 rows of seats, with 7 seats in each row. If the students seat themselves randomly, what is the probability that the 5th seat in the 4th row is empty?

  • A

    1/7

  • B

    1/6

  • C

    1/2

  • D

    1/5

Question 5

Two fair coins are tossed. It is known that at least one tail appears. What is the probability that both coins are tails?

  • A

    1/2

  • B

    1/3

  • C

    1/4

  • D

    2/3

Question 6

Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

  • A

    13/90

  • B

    12/90

  • C

    78/90

  • D

    77/90

Question 7

Consider a finite sequence of random values X = { x1, x2,..., xn}. Let μx be the mean and σx be the standard deviation of X. Let another finite sequence Y of equal length be derived from this as yi = a*xi + b, where a and b are positive constants. Let μy be the mean and σy be the standard deviation of this sequence. Which one of the following statements is INCORRECT?

  • A

    Index position of mode of X in X is the same as the index position of mode of Y in Y.

  • B

    Index position of median of X in X is the same as the index position of median of Y in Y.

  • C

    μy = aμx+b

  • D

    σy = aσx+b

Question 8

If the difference between expectation of the square of a random variable (E[X²]) and the square of the expectation of the random variable (E[X])² is denoted by R, then?

  • A

    R = 0

  • B

    R < 0

  • C

    R >= 0

  • D

    R > 0

Question 9

If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

  • A

    1/3

  • B

    1/4

  • C

    1/2

  • D

    2/3

Question 10

What is the probability that divisor of 1099 is a multiple of 1096?

  • A

    1/625

  • B

    4/625

  • C

    12/625

  • D

    16/625

There are 94 questions to complete.

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