Advertisements
Advertisements
प्रश्न
Mark the correct alternative in the following question:
Let X be a discrete random variable. Then the variance of X is
विकल्प
E(X2)
E(X2) + (E(X))2
E(X2) - (E(X))2
\[\sqrt{E\left( X^2 \right) - \left( E\left( X \right) \right)^2}\]
उत्तर
Since, the variance of a discrete random variable X is given by:
Var(X) = E(X2) - (E(X))2
APPEARS IN
संबंधित प्रश्न
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.
An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represents the number of black balls. What are the possible values of X? Is X a random variable?
Two numbers are selected at random (without replacement) from the first five positive integers. Let X denote the larger of the two numbers obtained. Find the mean and variance of X
A random variable X has the following probability distribution:
Values of X : | −2 | −1 | 0 | 1 | 2 | 3 |
P (X) : | 0.1 | k | 0.2 | 2k | 0.3 | k |
Find the value of k.
A random variable X has the following probability distribution:
Values of X : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
P (X) : | a | 3a | 5a | 7a | 9a | 11a | 13a | 15a | 17a |
Determine:
(i) The value of a
(ii) P (X < 3), P (X ≥ 3), P (0 < X < 5).
The probability distribution function of a random variable X is given by
xi : | 0 | 1 | 2 |
pi : | 3c3 | 4c − 10c2 | 5c-1 |
where c > 0 Find: c
Five defective bolts are accidently mixed with twenty good ones. If four bolts are drawn at random from this lot, find the probability distribution of the number of defective bolts.
Find the mean and standard deviation of each of the following probability distribution :
xi : | 1 | 2 | 3 | 4 |
pi : | 0.4 | 0.3 | 0.2 | 0.1 |
A discrete random variable X has the probability distribution given below:
X: | 0.5 | 1 | 1.5 | 2 |
P(X): | k | k2 | 2k2 | k |
Find the value of k.
Find the mean variance and standard deviation of the following probability distribution
xi : | a | b |
pi : | p | q |
A fair coin is tossed four times. Let X denote the longest string of heads occurring. Find the probability distribution, mean and variance of X.
A die is tossed twice. A 'success' is getting an odd number on a toss. Find the variance of the number of successes.
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) : |
\[\frac{1 - a}{4}\]
|
\[\frac{1 + 2a}{4}\]
|
\[\frac{1 - 2a}{4}\]
|
\[\frac{1 + a}{4}\]
|
If a random variable X has the following probability distribution:
X : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
P (X) : | a | 3a | 5a | 7a | 9a | 11a | 13a | 15a | 17a |
then the value of a is
If X is a random-variable with probability distribution as given below:
X = xi : | 0 | 1 | 2 | 3 |
P (X = xi) : | k | 3 k | 3 k | k |
The value of k and its variance are
Find the probability distribution of the number of doublets in three throws of a pair of dice and find its mean.
Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of spades. Hence, find the mean of the distribtution.
Five bad oranges are accidently mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, then find the probability distribution of number of bad oranges drawn. Hence find the mean and variance of the distribution.
Using the truth table verify that p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r).
Find mean and standard deviation of the continuous random variable X whose p.d.f. is given by f(x) = 6x(1 - x);= (0); 0 < x < 1(otherwise)
If p : It is a day time , q : It is warm
Give the verbal statements for the following symbolic statements :
(a) p ∧ ∼ q (b) p v q (c) p ↔ q
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 |
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).
A sample of 4 bulbs is drawn at random with replacement from a lot of 30 bulbs which includes 6 defective bulbs. Find the probability distribution of the number of defective bulbs.
A coin is biased so that the head is 3 times as likely to occur as tail. Find the probability distribution of number of tails in two tosses.
10 balls are marked with digits 0 to 9. If four balls are selected with replacement. What is the probability that none is marked 0?
State whether the following is True or False :
If r.v. X assumes the values 1, 2, 3, ……. 9 with equal probabilities, E(x) = 5.
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 :
The probability that a bomb will hit the target is 0.8. Find the probability that, out of 5 bombs, exactly 2 will miss the target.
Solve the following problem :
The probability that a machine will produce all bolts in a production run within the specification is 0.9. A sample of 3 machines is taken at random. Calculate the probability that all machines will produce all bolts in a production run within the specification.
Find the mean and variance of the number randomly selected from 1 to 15
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
Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a nonprime number. The probability that the card was drawn from Box I is ______.
A primary school teacher wants to teach the concept of 'larger number' to the students of Class II.
To teach this concept, he conducts an activity in his class. He asks the children to select two numbers from a set of numbers given as 2, 3, 4, 5 one after the other without replacement.
All the outcomes of this activity are tabulated in the form of ordered pairs given below:
2 | 3 | 4 | 5 | |
2 | (2, 2) | (2, 3) | (2, 4) | |
3 | (3, 2) | (3, 3) | (3, 5) | |
4 | (4, 2) | (4, 4) | (4, 5) | |
5 | (5, 3) | (5, 4) | (5, 5) |
- Complete the table given above.
- Find the total number of ordered pairs having one larger number.
- Let the random variable X denote the larger of two numbers in the ordered pair.
Now, complete the probability distribution table for X given below.
X 3 4 5 P(X = x) - Find the value of P(X < 5)
- Calculate the expected value of the probability distribution.