Advertisements
Advertisements
प्रश्न
The p.m.f. of a random variable X is
`"P"(x) = 1/5` , for x = I, 2, 3, 4, 5
= 0 , otherwise.
Find E(X).
उत्तर
E(X) = `sum_(i = 1)^5 x."P"(x)`
= `1 xx 1/5 + 2 xx 1/5 xx 3 xx 1/5 + 4 xx 1/5 + 5 xx 1/5`
= `15/5`
= 3
APPEARS IN
संबंधित प्रश्न
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
Which of the following distributions of probabilities of a random variable X are the probability distributions?
(i)
X : | 3 | 2 | 1 | 0 | −1 |
P (X) : | 0.3 | 0.2 | 0.4 | 0.1 | 0.05 |
X : | 0 | 1 | 2 |
P (X) : | 0.6 | 0.4 | 0.2 |
(iii)
X : | 0 | 1 | 2 | 3 | 4 |
P (X) : | 0.1 | 0.5 | 0.2 | 0.1 | 0.1 |
(iv)
X : | 0 | 1 | 2 | 3 |
P (X) : | 0.3 | 0.2 | 0.4 | 0.1 |
A class has 15 students whose ages are 14, 17, 15, 14, 21, 19, 20, 16, 18, 17, 20, 17, 16, 19 and 20 years respectively. One student is selected in such a manner that each has the same chance of being selected and the age X of the selected student is recorded. What is the probability distribution of the random variable X?
Find the probability distribution of Y in two throws of two dice, where Y represents the number of times a total of 9 appears.
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.
From a lot of 10 bulbs, which includes 3 defectives, a sample of 2 bulbs is drawn at random. Find the probability distribution of the number of defective bulbs.
Four balls are to be drawn without replacement from a box containing 8 red and 4 white balls. If X denotes the number of red balls drawn, then find the probability distribution of X.
Find the mean and standard deviation of each of the following probability distribution :
xi : | -5 | -4 | 1 | 2 |
pi : | \[\frac{1}{4}\] | \[\frac{1}{8}\] | \[\frac{1}{2}\] | \[\frac{1}{8}\] |
Find the mean and standard deviation of each of the following probability distribution:
xi : | −1 | 0 | 1 | 2 | 3 |
pi : | 0.3 | 0.1 | 0.1 | 0.3 | 0.2 |
A discrete random variable X has the probability distribution given below:
X: | 0.5 | 1 | 1.5 | 2 |
P(X): | k | k2 | 2k2 | k |
Determine the mean of the distribution.
In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.
Write the values of 'a' for which the following distribution of probabilities becomes a probability distribution:
X= xi: | -2 | -1 | 0 | 1 |
P(X= xi) : |
\[\frac{1 - a}{4}\]
|
\[\frac{1 + 2a}{4}\]
|
\[\frac{1 - 2a}{4}\]
|
\[\frac{1 + a}{4}\]
|
Mark the correct alternative in the following question:
For the following probability distribution:
X: | −4 | −3 | −2 | −1 | 0 |
P(X): | 0.1 | 0.2 | 0.3 | 0.2 | 0.2 |
The value of E(X) is
Mark the correct alternative in the following question:
Let X be a discrete random variable. Then the variance of X is
Three fair coins are tossed simultaneously. If X denotes the number of heads, find the probability distribution of X.
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 |
John and Mathew started a business with their capitals in the ratio 8 : 5. After 8 months, john added 25% of his earlier capital as further investment. At the same time, Mathew withdrew 20% of bis earlier capital. At the end of the year, they earned ₹ 52000 as profit. How should they divide the profit between them?
The defects on a plywood sheet occur at random with an average of the defect per 50 sq. ft. What Is the probability that such sheet will have-
(a) No defects
(b) At least one defect
[Use e-1 = 0.3678]
Amit and Rohit started a business by investing ₹20,000 each. After 3 months Amit withdrew ₹5,000 and Rohit put in ₹5,000 additionally. How should a profit of ₹12,800 be divided between them at the end of the year?
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.
The p.d.f. of r.v. of X is given by
f (x) = `k /sqrtx` , for 0 < x < 4 and = 0, otherwise. Determine k .
Determine c.d.f. of X and hence P (X ≤ 2) and P(X ≤ 1).
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 |
Determine whether each of the following is a probability distribution. Give reasons for your answer.
y | –1 | 0 | 1 |
P(y) | 0.6 | 0.1 | 0.2 |
A pair of dice is thrown 3 times. If getting a doublet is considered a success, find the probability of two successes
In a multiple choice test with three possible answers for each of the five questions, what is the probability of a candidate getting four or more correct answers by random choice?
Defects on plywood sheet occur at random with the average of one defect per 50 sq.ft. Find the probability that such a sheet has:
- no defect
- at least one defect
Use e−1 = 0.3678
Solve the following problem :
Find the probability of the number of successes in two tosses of a die, where success is defined as number greater than 4.
Solve the following problem :
In a large school, 80% of the students like mathematics. A visitor asks each of 4 students, selected at random, whether they like mathematics.
Find the probability that the visitor obtains the answer yes from at least 3 students.
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 ______.
Consider the probability distribution of a random variable X:
X | 0 | 1 | 2 | 3 | 4 |
P(X) | 0.1 | 0.25 | 0.3 | 0.2 | 0.15 |
Calculate `"V"("X"/2)`
The probability distribution of a random variable X is given below:
X | 0 | 1 | 2 | 3 |
P(X) | k | `"k"/2` | `"k"/4` | `"k"/8` |
Find P(X ≤ 2) + P (X > 2)
The random variable X can take only the values 0, 1, 2. Given that P(X = 0) = P(X = 1) = p and that E(X2) = E[X], find the value of p
Let X be a discrete random variable whose probability distribution is defined as follows:
P(X = x) = `{{:("k"(x + 1), "for" x = 1"," 2"," 3"," 4),(2"k"x, "for" x = 5"," 6"," 7),(0, "Otherwise"):}`
where k is a constant. Calculate Standard deviation of X.
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: The value of A if E(X) = 2.94
The probability distribution of a discrete random variable X is given below:
X | 2 | 3 | 4 | 5 |
P(X) | `5/"k"` | `7/"k"` | `9/"k"` | `11/"k"` |
The value of k is ______.
A person throws two fair dice. He wins ₹ 15 for throwing a doublet (same numbers on the two dice), wins ₹ 12 when the throw results in the sum of 9, and loses ₹ 6 for any other outcome on the throw. Then the expected gain/loss (in ₹) of the person is ______.
A random variable X has the following probability distribution:
x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(x) | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
Find:
- k
- P(X < 3)
- P(X > 4)