Advertisements
Advertisements
Question
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` |
Determine the value of k.
Solution
We know that P(0) + P(1) + P(2) + P(3) = 1
⇒ `"k" + "k"/2 + "k"/4 + "k"/8` = 1
⇒ `(8"k" + 4"k" + 2"k" + "k")/8` = 1
⇒ 15k = 8
∴ k = `8/15`
APPEARS IN
RELATED QUESTIONS
From a lot of 25 bulbs of which 5 are defective a sample of 5 bulbs was drawn at random with replacement. Find the probability that the sample will contain -
(a) exactly 1 defective bulb.
(b) at least 1 defective bulb.
Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as
(i) number greater than 4
(ii) six appears on at least one die
Three persons A, B and C shoot to hit a target. If A hits the target four times in five trials, B hits it three times in four trials and C hits it two times in three trials, find the probability that:
1) Exactly two persons hit the target.
2) At least two persons hit the target.
3) None hit the target.
Let, X denote the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given that
where k is a positive constant. Find the value of k. Also find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.
Find the probability distribution of the number of doublets in four throws of a pair of dice. Also find the mean and variance of this distribution.
Four cards are drawn simultaneously from a well shuffled pack of 52 playing cards. Find the probability distribution of the number of aces.
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.
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 |
Find the mean and standard deviation of each of the following probability distribution :
| xi : | 0 | 1 | 2 | 3 | 4 | 5 |
| pi : |
\[\frac{1}{6}\]
|
\[\frac{5}{18}\]
|
\[\frac{2}{9}\]
|
\[\frac{1}{6}\]
|
\[\frac{1}{9}\]
|
\[\frac{1}{18}\]
|
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.
Two cards are drawn simultaneously from a pack of 52 cards. Compute the mean and standard deviation of the number of kings.
If the probability distribution of a random variable X is as given below:
Write the value of P (X ≤ 2).
| X = xi : | 1 | 2 | 3 | 4 |
| P (X = xi) : | c | 2c | 4c | 4c |
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
A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P (X = 3) = 2 P (X = 1) and P (X = 2) = 0.3, then P (X = 0) is
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
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.
Calculate `"e"_0^circ ,"e"_1^circ , "e"_2^circ` from the following:
| Age x | 0 | 1 | 2 |
| lx | 1000 | 880 | 876 |
| Tx | - | - | 3323 |
The following data gives the marks of 20 students in mathematics (X) and statistics (Y) each out of 10, expressed as (x, y). construct ungrouped frequency distribution considering single number as a class :
(2, 7) (3, 8) (4, 9) (2, 8) (2, 8) (5, 6) (5 , 7) (4, 9) (3, 8) (4, 8) (2, 9) (3, 8) (4, 8) (5, 6) (4, 7) (4, 7) (4, 6 ) (5, 6) (5, 7 ) (4, 6 )
A fair coin is tossed 12 times. Find the probability of getting at least 2 heads .
Write the negation of the following statements :
(a) Chetan has black hair and blue eyes.
(b) ∃ x ∈ R such that x2 + 3 > 0.
If X ∼ N (4,25), then find P(x ≤ 4)
The probability that a bomb dropped from an aeroplane will strike a target is `1/5`, If four bombs are dropped, find the probability that :
(a) exactly two will strike the target,
(b) at least one will strike the target.
A random variable X has the following probability distribution :
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| P(X) | C | 2C | 2C | 3C | C2 | 2C2 | 7C2+C |
Find the value of C and also calculate the mean of this distribution.
The probability that a bulb produced by a factory will fuse after 200 days of use is 0.2. Let X denote the number of bulbs (out of 5) that fuse after 200 days of use. Find the probability of (i) X = 0, (ii) X ≤ 1, (iii) X > 1, (iv) X ≥ 1.
Let the p.m.f. of a random variable X be P(x) = `(3 - x)/10`, for x = −1, 0, 1, 2 = 0, otherwise Then E(x) is ______
Find the probability distribution of the number of doublets in three throws of a pair of dice
Find the mean and variance of the number randomly selected from 1 to 15
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 |
Variance of X.
Two biased dice are thrown together. For the first die P(6) = `1/2`, the other scores being equally likely while for the second die, P(1) = `2/5` and the other scores are equally likely. Find the probability distribution of ‘the number of ones seen’.
