Let n be greater than or equal to 2 be an integer Suppose a

Let n be greater than or equal to 2 be an integer. Suppose a random variable X_n has the probability mass function

f(x)=x/m_n , for 1,2,...,n

1. What is m_n?

2. Sketch a probability histogram for n = 5

3. Compute P(2 < X₅ <= 4).

4. Show that the distribution function of X₁₀₀ is F(x) = [x]([x]+1)=10100, for 1<= x<= 100, where [x]
is the greatest integer in x.

5. Compute  P(X₁₀₀ <= 50)

Solution