1. (4 marks) Check whether the mean and the variance of the following distribution exist: a. fx(x)=aπ(a2+x2)−∞&lt;x&lt;∞ (a is positive constant) b. fx(x)={2x−3x≥10else 2. (5 mark) Let X be a uniformly distributed random variable with probability density function: fx(x)={a−1&lt;x&lt;30else FInd the distribution for the random variable of Y=X2

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1. (4 marks) Check whether the mean and the variance of the following distribution exist: a. fx(x)=aπ(a2+x2)−∞&amp;lt;x&amp;lt;∞ (a is positive constant) b. fx(x)={2x−3x≥10else 2. (5 mark) Let X be a uniformly distributed random variable with probability density function: fx(x)={a−1&amp;lt;x&amp;lt;30else FInd the distribution for the random variable of Y=X2

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Step 1 Question 1: (a) Here fx(x) is pdf of Cauchy distribution and we know that mean and variance does not exist for Cauchy distribution, since E|X| does not exist for this pdf. (b) Mean exist in this case, but variance does not exist as E|X2| does not exist. Step 2 Question 2: The pdf of Y is fY(y)={ay,0&amp;lt;y&amp;lt;1a2y,1&amp;lt;y&amp;lt;9 where a=14

1. (4 marks) Check whether the mean and the variance of the following

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