Probability (ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern)): Questions 16 - 19 of 205

The moment generating function of an exponential random variable X with parameter λ (for t < 1/λ) is:

Suppose marks of students in a test are normally distributed. If the test has a mean of 100 and a standard deviation of 10, what is the probability that a student who gives the test will score between 90 and 110?

Patients are recruited onto the two arms (Control, Treatment) of a clinical trial. The probability that an adverse outcome occurs on the control arm is , and is for the treatment arm. Patients are allocated alternately onto the two arms, and their outcomes are independent. What is the probability that the first adverse event occurs on the control arm?

In describing the survival rate and life expectancy in a certain population, let denote the event of reaching the age of years and be the corresponding probability. If then, what is the probability that a 50 years old will die within 5 years?