A coin is tossed 5 times. The probability of head is 1/2. The probability of exactly 2 heads is
1/16
3/10
5/16
7/16
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
A discrete random variable X takes value from 1 to 5 with probabilities as shown in the table. A student calculate the mean of X as 3.5 and her teacher calculates the variance to X as 1.5 which of the following statement is true?

Both the student and the teacher are right
Both the student and the teacher are wrong
The student is wrong but the teacher is right
The student is right but the teacher is wrong
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
Find the missing probabilities given in the PMF table

x

2

3

4

P(X=x)

1/2

x

2x

1/6 ; 1/2
1/6 ; 2/6
4/5 ; 5/6
5/6 ; 7/4
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
Find the probability of the success, if getting 3 is termed as success when a dice is thrown ?
1/4
1/6
1/7
1/8
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is
1/32
2/32
6/32
3/32
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
The two sides of a fair coin are labeled as 0 and 1. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min (M, N), the expected value E(X) (rounded off to two decimal places) is _______
0.25
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
A discrete random variable X can take all possible integer values from 1 to K , each with a probability 1/k . Its variance is
( K^2 - 1)/12
(K-1)/2
K/2
(k+1)/5
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Let X be a random variable, and P(X=x) is the PMF given by,

Determine the value of k

0.1
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00

Let’s say that 80% of all business startups in the IT industry report that they generate a profit in their first year. If a sample of 10 new IT business startups is selected, find the probability that exactly seven will generate a profit in their first year. (rounded off to four decimal places)

0.2013
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00

Ten coins are thrown simultaneously. Find the probability of getting at least seven heads? (Round of to upto 3 decimals)

((0.171,0.172))
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00

Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66

[MSQ]

I is correct, II is incorrect.
Only one of them is correct.
Both are incorrect
Both are correct
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
The current (in mA) measured in a piece of copper wire is known to follow a uniform distribution over the interval [0, 25]. Write down the formula for the probability density function f(x) of the random variable X representing the current. Which of the following is/are correct?

Mean(X) = 13.5 mA
Mean(X) = 12.5 mA
Variance(X) = 52.08 mA^2
Variance(X) = 48.18 mA^2
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
A biased die is thrown thirty times in a game. Total of 8 sixes are seen till the point. If the die is thrown a further twelve times then which of the following is/are correct?
The probability that a six will occur exactly twice is 0.211
The expected number of sixes are 2.8
variance of the number of sixes is 2.347
None of them are correct
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
One dice was thrown. Let the random variable X be the number 6 shown by the dice face. Which of the following is/are correct?
CDF of X is given by

P(0 ≤ X < 2) = 0.98
P(−2 ≤ X < 1) = 5/6
A and C are correct.
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00