Probability Distribution for GATE

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Question 1

If X is a normal variate with mean 30 and standard deviation 5, what is Probability (26 =< X =< 34), given A (z = 0.8) = 0.2881 where A represents area.

  • 0.2881

  • 0.5762

  • 0.8181

  • 0.1616

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Question 2

For a random variable x (where : -∞ < x < ∞) following normal distribution, the mean is μ = 100. If the probability is P = α for x >= 110. Then the probability of x lying between 90 and 110 i.e. P(90 =< x =< 110) is equal to

  • 1 - 2α

  • 1 - α

  • 1 - α/2

  • 2α

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Question 3

What is the probability of observing exactly k successes in n trials in a binomial distribution with parameter p?

  • [Tex]^{n}C_{k}\,\,p^{k}(1-p)^{n-k}[/Tex]

  • [Tex]p^{k}(1-p)^{n-k}[/Tex]

  • [Tex]^{n}C_{k}\,\,p^{n}(1-p)^{k}[/Tex]

  • [Tex]p(1-p)^{k}[/Tex]

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Question 4

In an exponential distribution, the parameter λ represents:

  • The mean of the distribution

  • The standard deviation of the distribution

  • The probability of success on each trial

  • The rate parameter or average rate of occurrence of the event

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Question 5

What is the probability of observing exactly k successes in a Poisson distribution with parameter λ?

  • [Tex]\frac{e^{-\lambda}\lambda^{k}}{k!}[/Tex]

  • [Tex]\frac{{-\lambda}^{k}}{e^{-\lambda}}[/Tex]

  • [Tex]{e^{-\lambda}}[/Tex]

  • [Tex]\frac{e^{-\lambda}}{\lambda^{k}}[/Tex]

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Question 6

In a Poisson distribution, as the parameter λ increases:

  • The distribution becomes more symmetric

  • The variance decreases

  • The distribution becomes more skewed to the right

  • The mean increases

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Question 7

What is the main purpose of using a T-distribution instead of a standard normal distribution in hypothesis testing?

  • It provides a wider range of confidence intervals

  • It allows for the estimation of population parameters

  • It accounts for uncertainty due to small sample sizes

  • It simplifies calculations in statistical analysis

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Question 8

What happens to the mean of a geometric distribution as the probability of success (p) increases?

  • It increases

  • It decreases

  • It remains constant

  • It fluctuates

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Question 9

If Z is a standard normal random variable, what is P(Z < -1.5)?

  •  0.0668

  • 0.1587

  • 0.0228

  • 0.5

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Question 10

Which one of the following statements is not true?

  • The measure of skewness is dependent upon the amount of dispersion

  • In a symmetric distribution, the values of mean, mode and median are the same

  • In a positively skewed distribution, mean > median > mode

  • In a negatively skewed distribution, mode > mean > median

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There are 10 questions to complete.

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