Independent Random Variables MCQ Quiz in தமிழ் - Objective Question with Answer for Independent Random Variables - இலவச PDF ஐப் பதிவிறக்கவும்

The correct answer are option 1, 2, 3 & 4

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Explanation -

option (1) - Z also follows a normal distribution with mean 0 and standard deviation 1.

This is true because we've transformed X into Z scores by subtracting the mean and dividing by the standard deviation.

The mean of Z will be 0 and the standard deviation will be 1 by definition.

option (3) - X and Z are not independent random variables.

This is true because the value of Z directly depends on the value of X. If you know the value of X, you can determine the value of Z.

Thus, they are dependent random variables.

option (2) - The probability density function (PDF) of Z is the same as that of X.

This statement is false. Z and X do not share the same probability density function because the transformation changes the shape of the distribution.

Z follows a standard normal distribution (mean 0, standard deviation 1), while X follows a normal distribution with mean μ and standard deviation σ.

option (4) - The cumulative distribution function (CDF) of X is uniformly distributed.

This statement is false. The cumulative distribution function (CDF) of a normally distributed random variable is not uniform.

It will look like an S-shaped curve, not a straight line, which you would see in a uniform distribution.

Hence options (1) and (3) are correct.