Density function of normal distribution attains its maximum value when the value of random variable X is:

• A) All above
• B) X = Mean
• C) X = Standard Deviation
• D) X = Variance

A discrete probability function f(x) is always:

• A) Non-negative
• B) 1
• C) Negative
• D) 0

Which of the following is true for the Poisson distribution:

• A) mean > variance
• B) mean = variance
• C) mean = standard deviation
• D) mean > variance

For any probability density function, the TOTAL area under the curve is always:

• A) 0
• B) 1
• C) 0.75
• D) 0.5

If X and Y are independent, then Cov (X, Y) is equal to:

• A) 1
• B) 0
• C) 0 and 1
• D) None

An expected value of a random variable is equal to:

• A) Mean
• B) Standard deviation
• C) Quartile
• D) Variance

In a bivariate probability distribution of X and Y,
If f(1,1)=4/15, g(1)=2/3, h(1)=2/5,
then

• A) Both of these
• B) X and Y are statistically independent
• C) None of these
• D) X and Y are not statistically independent

For a continuous random variable X, P(X = x) is:

• A) 1
• B) undefined
• C) 0.5
• D) 0

In a binomial experiment ,probability of success changes on:

• A) 30th trial
• B) Each trial
• C) Second trial
• D) 10th trial

${\text{In}}\,{\text{a}}\,{\text{binomial}}\,{\text{distribution,formula}}\,{\text{of}}\,{\text{calculating}}\,s\tan {\text{dard deviation is}}$

• A) $\sqrt {npq}$
• B) $\sqrt {np}$
• C) $\sqrt {pq}$
• D) $\sqrt p$

The standard normal distribution has it mean and variance equal to:

• A) 0 and 1 respectively
• B) 0 and 0 respectively
• C) 1 and 1 respectively
• D) 1 and 0 respectively

In a hypergeometric distribution, the probability of success:

• A) Less than probability of failure
• B) Equal to probability of failure
• C) Remains constant from trial to trial
• D) Does not remain constant from trial to trial

The shape of the Poisson distribution is:

• A) J shaped
• B) U shaped
• C) Positively skewed
• D) Negatively skewed

If the second moment ratio is less than 3 the distribution will be:

• A) Leptokurtic
• B) Mesokurtic
• C) None of these
• D) Platykurtic

$${\text{For the Poisson distribution P(X = 1) = }}\frac{{{e^{ - 0.135}}{{0.135}^1}}}{{1!}}{\text{ the mean value is:}}$$

• A) 0.135
• B) 1
• C) $${{e^{ - 0.135}}}$$
• D) -0.135

If b(x; 15, 0.75), the mean of this distribution is:

• A) 11.25
• B) 11.20
• C) 11.50
• D) 11.15

The cumulative distribution function F(x) for a continuous random variable X is the area under the density curve to the __________ of x.

• A) Center
• B) Right
• C) Left
• D) None of the above

If total probability of joint probability distribution f(x,y) is ONE then what will be the total probability of its marginal pdf h(y)?

• A) One
• B) Less than one
• C) Depend on given values
• D) Anywhere between zero and one

P (|X| < 1.5) =

• A) P(X > 1.5)
• B) P (-1.5 < X < 1.5)
• C) P(X = 1.5)
• D) P(X < 1.5)

$${\text{For the Poisson distribution P(X = 1) = }}\frac{{{e^{ - 2}}{2^1}}}{{1!}}{\text{ the mean value is:}}$$

• A) 0
• B) 2
• C) 1
• D) 3