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Question type / Difficulty / Years (37)
Q1
Let and be two independent random variables with , , and . Find the value of .
Integer answer
Q2
The probability mass function of a discrete random variable is given by the table. Find the value of such that . Enter the answer correct to one decimal place.
Integer answer
Q3
Using Markov's inequality, find an upper bound on the probability that the processing time is at least times its expected value.
Comprehension
Q4
Using Chebyshev's inequality, find a lower bound on the probability that the processing time lies between milliseconds and milliseconds. Enter the answer correct to two decimal places.
Comprehension
Q5
Let be the number of items produced by a machine on a given day with and . Using Chebyshev's inequality, find a lower bound on the probability that a machine produces between and items on a given day.
Single correct
Q6
What is the expected payment that the designer earns for a randomly chosen project?
Comprehension
Q7
Using Markov's inequality, find an upper bound on the probability that the designer earns at least Rs. . Enter the answer correct up to three decimal places.
Comprehension
Q8
Calculate the value of .
Comprehension
Q9
Find the correlation coefficient between and . Enter the answer correct up to two decimal places.
Comprehension
Q10
A call center analyst monitors the number of calls received at the centre daily. Let denote the number of calls received in a day. Using Markov's inequality, the analyst determines an upper bound of on the probability of receiving more than calls. Calculate the mean of .
Integer answer
Q11
What is the value of ?
Comprehension
Q12
Find the expected amount of money to be gained. Enter the answer correct to two decimal places.
Comprehension
Q13
Find . Enter the answer correct to two decimal places.
Comprehension
Q14
What is the value of ? Enter the answer correct to two decimal places.
Comprehension
Q15
Find the value of .
Comprehension
Q16
What is the value of ?
Comprehension
Q17
Using Markov's inequality, find an upper bound on the probability that production will exceed on a given day. Enter the answer correct to one decimal place.
Comprehension
Q18
Using Chebyshev's inequality, find a lower bound on the probability that on a given day production will be between and .
Comprehension
Q19
The joint PMF of two discrete random variables and is given in the following table. Find the value of . Enter the answer correct to two decimal places.
Integer answer
Q20
Consider bits , where each bit is equally likely to be or , and is independent of all other bits. Define bits , . Let and be, respectively, the number of s in and . Assuming , what is the expected value of and ?
Single correct
Q21
Using Markov inequality, find an upper bound to the probability . Which values below are greater than or equal to that upper bound?
Comprehension
Q22
Using Chebyshev's inequality, find an upper bound to the probability that at least people attended the interview. Enter the answer correct to one decimal place.
Comprehension
Q23
Find the expected value of . Enter the answer correct to two decimal places.
Integer answer
Q24
Suppose and are independent random variables with means and , and variances and , respectively. Find the value of . Hint: If and are independent, then and are also independent.
Single correct
Q25
The probability distribution of a discrete random variable is given below. Calculate the expected value of . Enter the answer correct to one decimal place.
Integer answer
Q26
Using Markov's inequality, find a bound on the probability that this week's production will exceed .
Comprehension
Q27
Using Chebyshev's inequality, find a lower bound on the probability that this week's production will be between and . Enter the answer correct to two decimal places.
Comprehension
Q28
The joint PMF of two discrete random variables and is given in the following table. Find the value of .
Integer answer
Q29
Find the expected value of . Enter the answer correct to one decimal place.
Comprehension
Q30
Using Chebyshev's inequality, find a lower bound for , where and are mean and variance of , respectively. Enter the answer correct to two decimal places.
Integer answer
Q31
The probability mass function of a random variable is given as. Define . Find the expected value of .
Integer answer
Q32
Find the expected number of girls selected for the committee. Enter the answer correct to two decimal places.
Comprehension
Q33
Using Chebyshev’s inequality, find a lower bound for , where and are mean and variance of . Enter the answer correct to decimal places.
Comprehension
Q34
Let be a Poisson random variable with mean equal to . Which of the following bounds can be obtained using Markov’s inequality?
Single correct
Q35
The joint PMF of two discrete random variables and is given in the following table. Calculate . Enter the answer correct to two decimal places.
Integer answer
Q36
Use Markov's inequality to find an upper bound on . Enter the answer correct to two decimal places.
Integer answer
Q37
Use Chebyshev's inequality to find a lower bound on . Enter the answer correct to two decimal places.
Integer answer
Showing 37 questions.