Advertisements
Advertisements
Question
Let X be a discrete random variable. The probability distribution of X is given below:
X | 30 | 10 | – 10 |
P(X) | `1/5` | `3/10` | `1/2` |
Then E(X) is equal to ______.
Options
6
4
3
– 5
Solution
Let X be a discrete random variable. The probability distribution of X is given below:
X | 30 | 10 | – 10 |
P(X) | `1/5` | `3/10` | `1/2` |
Then E(X) is equal to 4.
Explanation:
E(X) = `30 xx 1/5 + 10 xx 3/10 - 10 xx 1/2` = 4.
APPEARS IN
RELATED QUESTIONS
From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution.
State the following are not the probability distributions of a random variable. Give reasons for your answer.
X | 0 | 1 | 2 |
P (X) | 0.4 | 0.4 | 0.2 |
Find the probability distribution of number of heads in two tosses of a coin.
Find the probability distribution of number of heads in four tosses of a coin.
Two numbers are selected at random (without replacement) from positive integers 2, 3, 4, 5, 6 and 7. Let X denote the larger of the two numbers obtained. Find the mean and variance of the probability distribution of X.
Let X be a random variable which assumes values x1, x2, x3, x4 such that 2P (X = x1) = 3P(X = x2) = P (X = x3) = 5 P (X = x4). Find the probability distribution of X.
Three cards are drawn successively with replacement from a well-shuffled deck of 52 cards. A random variable X denotes the number of hearts in the three cards drawn. Determine the probability distribution of X.
Two cards are drawn simultaneously from a well-shuffled deck of 52 cards. Find the probability distribution of the number of successes, when getting a spade is considered a success.
Find the mean and standard deviation of each of the following probability distributions:
xi : | 2 | 3 | 4 |
pi : | 0.2 | 0.5 | 0.3 |
Find the mean and standard deviation of each of the following probability distribution:
xi : | 1 | 3 | 4 | 5 |
pi: | 0.4 | 0.1 | 0.2 | 0.3 |
Find the mean and standard deviation of each of the following probability distribution :
xi : | -3 | -1 | 0 | 1 | 3 |
pi : | 0.05 | 0.45 | 0.20 | 0.25 | 0.05 |
Three cards are drawn at random (without replacement) from a well shuffled pack of 52 cards. Find the probability distribution of number of red cards. Hence, find the mean of the distribution .
For what value of k the following distribution is a probability distribution?
X = xi : | 0 | 1 | 2 | 3 |
P (X = xi) : | 2k4 | 3k2 − 5k3 | 2k − 3k2 | 3k − 1 |
A random variable has the following probability distribution:
X = xi : | 1 | 2 | 3 | 4 |
P (X = xi) : | k | 2k | 3k | 4k |
Write the value of P (X ≥ 3).
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes and, hence, find its mean.
Compute the age specific death rate for the following data :
Age group (years) | Population (in thousands) | Number of deaths |
Below 5 | 15 | 360 |
5-30 | 20 | 400 |
Above 30 | 10 | 280 |
A fair coin is tossed 12 times. Find the probability of getting at least 2 heads .
Alex spends 20% of his income on food items and 12% on conveyance. If for the month of June 2010, he spent ₹900 on conveyance, find his expenditure on food items during the same month.
Verify whether the following function can be regarded as probability mass function (p.m.f.) for the given values of X :
X | -1 | 0 | 1 |
P(X = x) | -0.2 | 1 | 0.2 |
Solve the following:
Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.
A highway safety group is interested in studying the speed (km/hrs) of a car at a check point.
Determine whether each of the following is a probability distribution. Give reasons for your answer.
x | 0 | 1 | 2 |
P(x) | 0.4 | 0.4 | 0.2 |
A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. If X denotes the age of a randomly selected student, find the probability distribution of X. Find the mean and variance of X.
There are 10% defective items in a large bulk of items. What is the probability that a sample of 4 items will include not more than one defective item?
Solve the following problem :
Following is the probability distribution of a r.v.X.
X | – 3 | – 2 | –1 | 0 | 1 | 2 | 3 |
P(X = x) | 0.05 | 0.1 | 0.15 | 0.20 | 0.25 | 0.15 | 0.1 |
Find the probability that X is positive.
Solve the following problem :
It is observed that it rains on 10 days out of 30 days. Find the probability that it rains on exactly 3 days of a week.
For the random variable X, if V(X) = 4, E(X) = 3, then E(x2) is ______
The probability distribution of a discrete random variable X is given as under:
X | 1 | 2 | 4 | 2A | 3A | 5A |
P(X) | `1/2` | `1/5` | `3/25` | `1/10` | `1/25` | `1/25` |
Calculate: Variance of X
If the p.m.f of a r. v. X is
P(x) = `c/x^3`, for x = 1, 2, 3
= 0, otherwise
then E(X) = ______.
The probability that a bomb will hit the target is 0.8. Complete the following activity to find, the probability that, out of 5 bombs exactly 2 will miss the target.
Solution: Here, n = 5, X =number of bombs that hit the target
p = probability that bomb will hit the target = `square`
∴ q = 1 - p = `square`
Here, `X∼B(5,4/5)`
∴ P(X = x) = `""^"n""C"_x"P"^x"q"^("n" - x) = square`
P[Exactly 2 bombs will miss the target] = P[Exactly 3 bombs will hit the target]
= P(X = 3)
=`""^5"C"_3(4/5)^3(1/5)^2=10(4/5)^3(1/5)^2`
∴ P(X = 3) = `square`