MTH302

1. For a binomial distribution where $n = 5$ , if $P (X = 4) = P (X = 3)$ , then $p =$ :

a)

\frac{1}{3}

b)

\frac{3}{4}

c)

1

d)

\frac{2}{3}

2. For a binomial distribution with $n = 4$ , given $P (X = 0) = \frac{16}{81}$ , find $P (X = 4)$ :

a)

\frac{1}{16}

b)

\frac{1}{81}

c)

\frac{1}{27}

d)

\frac{1}{8}

3. The probability of a shooter hitting a target is $\frac{3}{4}$ . How many minimum times must he fire so that the probability of hitting the target at least once is more than 0.99?

a) 2 b) 3 c) 4 d) 5

4. Which of the following cannot be a possible value of mean and variance for a binomial distribution?

a) Mean = 8, Variance = 4.5 b) Mean =

\frac{28}{5}

, Variance =

\frac{121}{25}

c) Mean = 4, Variance = 5 d) Mean = 15, Variance = 6

5. The probability of getting 4 tails in 6 tosses of a fair coin is:

a)

\frac{15}{64}

b) 1 c)

\frac{15}{65}

d)

\frac{13}{70}

6. A binomial variable $X$ satisfies the relation $P (X = 2) = P (X = 3)$ . Find the value of the parameter $p$ . (if n=5):

a) 1 b)

\frac{1}{2}

c)

\frac{1}{3}

d)

\frac{1}{4}

7. The mean and variance of a binomial distribution are given as 2 and $\frac{4}{3}$ , respectively. What is the probability of getting no success?

a)

\frac{64}{729}

b)

\frac{128}{243}

c)

\frac{16}{243}

d)

\frac{15}{512}

8. If $X 1, X 2, X 3, X 4, X 5$ are Bernoulli trials with probability $p = 0.4$ , what is the expected value of their sum?

a) 2 b) 5 c) 3 d) 4

9. If $X 1, X 2, X 3, X 4, X 5$ are Bernoulli trials with probability $p = 0.6$ , what is the variance of their sum?

a) 2.4 b) 4.2 c) 1.52 d) 1.2

10. If the moment-generating function of a distribution is given by:

$M (t) = 0.2 + 0.8 e^{t}$

What is the variance of the distribution?

a) 0.8 b) 1.62 c) 0.16 d) 0.32

MCQ on Binomial Distribution and Bernoulli Trials

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