Advertisements
Advertisements
Question
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 non-negative
Solution
P(X is non-negative)
= P(X = 0 or X = 1 or X = 2 or X = 3)
= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= 0.20 + 0. 25 + 0.15 + 0.10 = 0.70
APPEARS IN
RELATED QUESTIONS
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 |
An urn contains 25 balls of which 10 balls bear a mark ‘X’ and the remaining 15 bear a mark ‘Y’. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability that
(i) all will bear ‘X’ mark.
(ii) not more than 2 will bear ‘Y’ mark.
(iii) at least one ball will bear ‘Y’ mark
(iv) the number of balls with ‘X’ mark and ‘Y’ mark will be equal.
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
Find the probability distribution of the number of heads, when three coins are tossed.
Find the probability distribution of the number of white balls drawn in a random draw of 3 balls without replacement, from a bag containing 4 white and 6 red balls
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.
Let X represent the difference between the number of heads and the number of tails when a coin is tossed 6 times. What are the possible values of X?
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.
The probability distribution of a random variable X is given below:
x | 0 | 1 | 2 | 3 |
P(X) | k |
\[\frac{k}{2}\]
|
\[\frac{k}{4}\]
|
\[\frac{k}{8}\]
|
Determine P(X ≤ 2) and P(X > 2) .
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: | 0 | 1 | 3 | 5 |
pi : | 0.2 | 0.5 | 0.2 | 0.1 |
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 |
Find the mean and standard deviation of each of the following probability distribution :
xi : | 0 | 1 | 2 | 3 | 4 | 5 |
pi : |
\[\frac{1}{6}\]
|
\[\frac{5}{18}\]
|
\[\frac{2}{9}\]
|
\[\frac{1}{6}\]
|
\[\frac{1}{9}\]
|
\[\frac{1}{18}\]
|
Two cards are drawn simultaneously from a pack of 52 cards. Compute the mean and standard deviation of the number of kings.
Two cards are selected at random from a box which contains five cards numbered 1, 1, 2, 2, and 3. Let X denote the sum and Y the maximum of the two numbers drawn. Find the probability distribution, mean and variance of X and Y.
In roulette, Figure, the wheel has 13 numbers 0, 1, 2, ...., 12 marked on equally spaced slots. A player sets Rs 10 on a given number. He receives Rs 100 from the organiser of the game if the ball comes to rest in this slot; otherwise he gets nothing. If X denotes the player's net gain/loss, find E (X).
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 .
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.
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:
The probability distribution of a discrete random variable X is given below:
X: | 2 | 3 | 4 | 5 |
P(X): |
\[\frac{5}{k}\]
|
\[\frac{7}{k}\]
|
\[\frac{9}{k}\]
|
\[\frac{11}{k}\] |
The value of k is .
Three different aeroplanes are to be assigned to carry three cargo consignments with a view to maximize profit. The profit matrix (in lakhs of ₹) is as follows :
Aeroplanes | Cargo consignments | ||
C1 | C2 | C3 | |
A1 | 1 | 4 | 5 |
A2 | 2 | 3 | 3 |
A3 | 3 | 1 | 2 |
How should the cargo consignments be assigned to the aeroplanes to maximize the profit?
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.
Find the premium on a property worth ₹12,50,000 at 3% if the property is fully insured.
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?
A random variable X has the following probability distribution :
x = x | 0 | 1 | 2 | 3 | 7 | |||
P(X=x) | 0 | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
Determine (i) k
(ii) P(X> 6)
(iii) P(0<X<3).
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 die is thrown 4 times. If ‘getting an odd number’ is a success, find the probability of at most 2 successes.
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.
Solve the following problem :
The probability that a component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 components tested survive.
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.
Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X and variance of X
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)`
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’.
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
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 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
The probability distribution of a random variable x is given as under:
P(X = x) = `{{:("k"x^2, "for" x = 1"," 2"," 3),(2"k"x, "for" x = 4"," 5"," 6),(0, "otherwise"):}`
where k is a constant. Calculate E(X)
For the following probability distribution:
X | 1 | 2 | 3 | 4 |
P(X) | `1/10` | `3/10` | `3/10` | `2/5` |
E(X2) is equal to ______.
Find the probability distribution of the number of successes in two toves of a die where a success is define as:- Six appeared on at least one die.
A random variable x has to following probability distribution.
X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(x) | 0 | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
Determine