List of top Economics Questions on Random variables

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: A random variable is a numerical description of the outcome of an experiment. Reason R: The particular numerical value of a random variable does not depend on the outcome of the experiment.
Suppose that the random variable \( X \) takes on the values: -1, 0, and 2 with probabilities \( \frac{1}{8} \), \( \frac{1}{2} \), and \( \frac{3}{8} \) respectively. Find the expected value of \( X \).

If the probability function for a random variable \( x \) is given as \( f(x) = \frac{x+3}{15} \) when \( x = 1, 2, 3 \), find the sum of the values of the probability distribution for \( x \).

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: For a random variable X which has mean = 10 and variance = 100. the variance of (5x+10) is 2500.
Reason R: Var(ax+b) = Var(x)
and so the variance of (ax+b)
or Var(5x+10) is 100.
In the light of the above statements, choose the correct answer from the options given below:
The possible inflection points for \(f(x)=\frac{1}{9}x^3-\frac{1}{6}x^2-\frac{2}{3}x+1\) is/are:
Find \(\frac{dy}{dx}\) if \(x\sqrt{1+y}+y\sqrt{1+x}=0.\)
For a random variable X, E(X-μ)4 = 16 [where μ = E(X)] and E(X-μ)2 = 2. What is the value of Kurtosis for this variable?
\(\int(\frac{e^{8\text{ln}x}-e^{4\text{ln}x}}{e^{4\text{ln}x}-e^{2\text{ln}x}})dx\)