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QUESTION: 1

If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A ∩ B)

Solution:

We have ,

P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4

QUESTION: 2

If S is the sample space associated with a random experiment. Then a real valued function which assign to each element of S, a unique real number is called a ……

Solution:

QUESTION: 3

Random variable is a real valued function whose domain is the sample space of a ……… and range is the set of ………

Solution:

A random variable is a numerical description of the outcome of a statistical experiment. It can be any outcome from some chance process, like how many heads will occur in a series of 20 flips etc. So as it is related to the chance of an event. Therefore its domain is the sample space of random experiment and as chance of occuring can never be a fraction or a negative number. So range is the set of real numbers.

QUESTION: 4

The probability distribution of the number of heads in three tosses of a coin is:

Solution:

QUESTION: 5

A random variable X has the following probability distribution:

Then k =?

Solution:

QUESTION: 6

An urn contains 3 red and 2 black balls. Two balls are randomly drawn. Let X represents the number of black balls. The possible values of X are:

Solution:

The number of ways in which two balls can be represented are {(RR), (RB), (BR), (BB)}

Let X represent the number of black balls. Possible values of X are:

X (RR) = 0, X (RB) = 1,

X(BR) 1 and X (BB) = 2.

Therefore the possible values of X are 0, 1 and 2.

QUESTION: 7

A random variable X has the probability distribution:

Then the value of k is:

Solution:

QUESTION: 8

If a random variable X assumes all possible values in a given interval, then it is called ………

Solution:

As we known that a random variable which can assume all possible values within a given interval is called a continuous random variable.

QUESTION: 9

A random variable X has the probability distribution:

Then the value P(X ≥ 5) is:

Solution:

P(5) = 0.01, P(6) = 0.02, P(7) = 0.17

P(X ≥ 5) = P(5) + P(6) + P(7)

= 0.01 + 0.02 + 0.17

= 0.20

QUESTION: 10

If a random variable X assume values x_{1}, x_{2}, x_{3}, …, x_{n} with the corresponding probabilities p_{1}, p_{2}, p_{3}, …, p_{n}. Then

Solution:

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