A random variable X is uniformly distributed over the interval [2,10]. What is the probability that X takes a value between 4 and 8?

• A) 1
• B) 0.50
• C) 0.75
• D) 0.25

Exponential distribution is a Bivariate distribution

• A) False
• B) True
• C)
• D)

A mobile conversation follows an exponential distribution $f(x)=\frac{1}{3}e^\frac{-x}{3}$ . What is the probability that the conversation takes more than 5 times?

• A) $5e^{-15}$
• B) $e^{-1/3}$
• C) $e^{-3/5}$
• D) $e^{-5/3}$

The multinomial distribution is a generalization of which distribution?

• A) Binomial distribution
• B) Normal distribution
• C) Geometric distribution
• D) Poisson distribution

The pdf of poisson distribution is

• A) \( \frac{e^{-m}x!}{m^x}\)
• B) \(\frac{x!}{m^xe^{-m}}\)
• C) \(\frac{e^{-m}m^x}{x!}\)
• D) \(\frac{e^m m^x}{x!}\)

If ‘m’ is the mean of Poisson Distribution, the P(0) is given by ___________

• A) em
• B) e-m
• C) m-e
• D) e

Job arrive at a facility at an average rate of 5 in an 8 hour shift. The arrival of the jobs follows poisson distribution. The average service time of the job on the facility is 40 minutes. The service time follows an exponential distribution. Idle time(in hours) at a facility per shift will be

• A) \(\frac{14}{3}\)
• B) \(\frac{5}{7}\)
• C) \(\frac{10}{3}\)
• D) \(\frac{7}{5}\)

Which of the following is a key assumption of the multinomial distribution?

• A) All trials are dependent.
• B) Each trial has only two outcomes.
• C) The probabilities of all outcomes change with each trial.
• D) The number of trials is fixed.

A mobile conversation follows an exponential distribution f(x)=\frac{1}{3}e^\frac{-x}{3} . What is the probability that the conversation takes more than 5 times?

• A) 5e^{-15}
• B) e^{-3/5}
• C) e^{-5/3}
• D) e^{-1/3}

Which of the following real-life situations is best modeled by a multinomial distribution?

• A) Measuring temperature every hour
• B) Tossing a fair coin 10 times
• C) Recording the number of customers ordering coffee, tea, or juice in a café
• D) Counting the number of rainy days in a month

Poisson distribution is applied for ___________

• A) Continuous Random Variable
• B) Irregular Random Variable
• C) Uncertain Random Variable
• D) Discrete Random Variable

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is \mu. and the standard deviation for this distribution is given by

• A) \mu^2
• B) \mu
• C) \sqrt\mu
• D) \frac{1}{\mu}

In a survey, people choose their favorite fruit among apple, banana, orange, and grapes. If 200 people respond, which distribution best models the number of votes each fruit receives?

• A) Uniform Distribution
• B) Normal Distribution
• C) Hypergeometric Distribution
• D) Multinomial Distribution

In a Poisson Distribution, if mean (m) = e, then P(x) is given by ___________

• A) \frac{x!}{e^{(m-x)}}
• B) \frac{e^{(m-x)}}{x!}
• C) \frac{e^{(x-m)}}{x!}
• D) \frac{x!}{e^{(x-m)}}

A bag contains red, blue, and green balls. If 15 balls are drawn with replacement and color is recorded each time, what is the most appropriate distribution?

• A) Exponential Distribution
• B) Poisson Distribution
• C) Binomial Distribution
• D) Multinomial Distribution

Mean and variance of the poisson distribution are

• A) less than
• B) equal
• C) not equal
• D) greater than

A random variable X has an exponential distribution with probability distribution function is given by f(x)= 3e-3x for x>0 = 0 otherwise Find probability that X is not less than 2?

• A) e-3
• B) e-6
• C) e-6-1
• D) e-6 -3

A mobile conversation follows an exponential distribution \(f(x)=\frac{1}{3}e^\frac{-x}{3}\) . What is the probability that the conversation takes more than 5 times?

• A) \(e^{-1/3}\)
• B) \(e^{-3/5}\)
• C) \(5e^{-15}\)
• D) \(e^{-5/3}\)

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is \(\mu\). and the standard deviation for this distribution is given by

• A) \(\mu^2\)
• B) \(\mu\)
• C) \(\sqrt\mu\)
• D) \(\frac{1}{\mu}\)