Calculate the mean and standard deviation of the discrete probability distribution (round to 3 decimal places when necessary):

Analyze the scenario and complete the following: 

Complete the discrete probability distribution for the given variable. 

Calculate the expected value and variance of the discrete probability distribution. 

The value of a ticket in a small hospital lottery, in which 2.000 tickets are sold, with 1 grand prize of $2,500, 10 first prizes of $200, 20 second prizes of $125, and 65 third prizes of $30.

Complete the discrete probability distribution for the given variable. 

Calculate the expected value and variance of the discrete probability distribution. 

Out of 14 nurse practitioners who are on call on a given day, 4 are sick. If two on-call nurse practitioners are called in based on a random selection, determine the probability distribution for the number of sick nurse practitioners who are called in.

PO 0 0.1 5 0.09 10 0.11 15 0.11 20 25 0.14 0.12 30 0.12 35 0.1 40 0.11