Advertisements
Advertisements
प्रश्न
If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P (X ≤ 5).
उत्तर
\[\text{ Mean} (np) = 3 \text{ and variance } (npq) = \frac{3}{2}\]
\[ \therefore q = \frac{1}{2}\]
\[\text{ and } p = 1 - \frac{1}{2}\]
\[n = \frac{Mean}{p}\]
\[ \Rightarrow n = 6\]
\[\text{ Hence, the distribution is given by } \]
\[P(X = r) = ^{6}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{6 - r} , r = 0, 1, 2 . . . 6\]
\[ = \frac{^{6}{}{C}_r}{2^6} \]
\[ \therefore P(X \leq 5) = 1 - P(X = 6) \]
\[ = 1 - \frac{1}{64}\]
\[ = \frac{63}{64}\]
APPEARS IN
संबंधित प्रश्न
Given X ~ B (n, p)
If n = 10 and p = 0.4, find E(X) and var (X).
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
A couple has two children, Find the probability that both children are males, if it is known that at least one of the children is male.
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
A fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times.
Five cards are drawn one by one, with replacement, from a well-shuffled deck of 52 cards. Find the probability that
(i) all the five cards diamonds
(ii) only 3 cards are diamonds
(iii) none is a diamond
If getting 5 or 6 in a throw of an unbiased die is a success and the random variable X denotes the number of successes in six throws of the die, find P (X ≥ 4).
Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?
An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of successes.
The mathematics department has 8 graduate assistants who are assigned to the same office. Each assistant is just as likely to study at home as in office. How many desks must there be in the office so that each assistant has a desk at least 90% of the time?
An unbiased coin is tossed 8 times. Find, by using binomial distribution, the probability of getting at least 6 heads.
Suppose that a radio tube inserted into a certain type of set has probability 0.2 of functioning more than 500 hours. If we test 4 tubes at random what is the probability that exactly three of these tubes function for more than 500 hours?
Suppose X has a binomial distribution with n = 6 and \[p = \frac{1}{2} .\] Show that X = 3 is the most likely outcome.
How many times must a man toss a fair coin so that the probability of having at least one head is more than 80% ?
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.
From a lot of 30 bulbs that includes 6 defective bulbs, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
Find the binomial distribution when the sum of its mean and variance for 5 trials is 4.8.
The probability that an item produced by a factory is defective is 0.02. A shipment of 10,000 items is sent to its warehouse. Find the expected number of defective items and the standard deviation.
A dice is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of successes.
A die is thrown three times. Let X be 'the number of twos seen'. Find the expectation of X.
If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.
If the mean and variance of a binomial distribution are 4 and 3, respectively, find the probability of no success.
In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?
A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire in order to have more than 50% chance of hitting it at least once is
A fair die is tossed eight times. The probability that a third six is observed in the eighth throw is
Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 is
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that none is a spade ?
For X ~ B(n, p) and P(X = x) = `""^8"C"_x(1/2)^x (1/2)^(8 - x)`, then state value of n and p
If x4 occurs in the tth term in the expansion of `(x^4 + 1/x^3)^15`, then the value oft is equal to:
If the coefficients of x7 and x8 in `(2 + x/3)^n` are equal, then n is
If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then `(P(X = 2))/(P(X = 3))` is equal to ______.
A fair coin is tossed 6 times. Find the probability of getting heads 4 times.
If the sum of mean and variance of a binomial distribution is `25/9` for 5 trials, find p.
