Advertisements
Advertisements
प्रश्न
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: P (1 < X ≤ 2)
उत्तर
P (1 < X ≤ 2)
\[= P\left( X = 2 \right)\]
\[ = 5c - 1\]
\[ = \frac{5}{3} - 1\]
\[ = \frac{5 - 3}{3}\]
\[ = \frac{2}{3}\]
APPEARS IN
संबंधित प्रश्न
Probability distribution of X is given by
X = x | 1 | 2 | 3 | 4 |
P(X = x) | 0.1 | 0.3 | 0.4 | 0.2 |
Find P(X ≥ 2) and obtain cumulative distribution function of X
Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is hostler?
State the following are not the probability distributions of a random variable. Give reasons for your answer.
Z | 3 | 2 | 1 | 0 | -1 |
P(Z) | 0.3 | 0.2 | 0.4 | 0.1 | 0.05 |
From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. 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. If the coin is tossed twice, find the probability distribution of number of tails.
A random variable X has the following probability distribution.
X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(X) | 0 | k | 2k | 2k | 3k | k2 |
2k2 |
7k2 + k |
Determine
(i) k
(ii) P (X < 3)
(iii) P (X > 6)
(iv) P (0 < X < 3)
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
Five defective mangoes are accidently mixed with 15 good ones. Four mangoes are drawn at random from this lot. Find the probability distribution of the number of defective mangoes.
Two dice are thrown together and the number appearing on them noted. X denotes the sum of the two numbers. Assuming that all the 36 outcomes are equally likely, what is the probability distribution of X?
Two cards are drawn successively without replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces.
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
Find the probability distribution of Y in two throws of two dice, where Y represents the number of times a total of 9 appears.
Find the mean and standard deviation of each of the following probability distribution:
xi : | 1 | 3 | 4 | 5 |
pi: | 0.4 | 0.1 | 0.2 | 0.3 |
Find the mean and standard deviation of each of the following probability distribution :
xi : | -2 | -1 | 0 | 1 | 2 |
pi : | 0.1 | 0.2 | 0.4 | 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 |
Two bad eggs are accidently mixed up with ten good ones. Three eggs are drawn at random with replacement from this lot. Compute the mean for the number of bad eggs drawn.
An urn contains 5 red and 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls drawn. What are the possible values of X ? Is X a random variable ? If yes, then find the mean and variance of X.
A random variable X has the following probability distribution:
X : | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
P (X) : | 0.15 | 0.23 | 0.12 | 0.10 | 0.20 | 0.08 | 0.07 | 0.05 |
For the events E = {X : X is a prime number}, F = {X : X < 4}, the probability P (E ∪ F) is
Mark the correct alternative in the following question:
Let X be a discrete random variable. Then the variance of X is
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.
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 )
Verify the following function, which can be regarded as p.m.f. for the given values of X :
X = x | -1 | 0 | 1 |
P(x) | -0.2 | 1 | 0.2 |
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?
A fair coin is tossed 12 times. Find the probability of getting at least 2 heads .
The expenditure Ec of a person with income I is given by Ec = (0.000035) I2 + (0. 045) I. Find marginal propensity to consume (MPC) and average propensity to consume (APC) when I = 5000.
From the following data, find the crude death rates (C.D.R.) for Town I and Town II, and comment on the results :
Age Group (in years) | Town I | Town II | ||
Population | No. of deaths | Population | No. of deaths | |
0-10 | 1500 | 45 | 6000 | 150 |
10-25 | 5000 | 30 | 6000 | 40 |
25 - 45 | 3000 | 15 | 5000 | 20 |
45 & above | 500 | 22 | 3000 | 54 |
The p.d.f. of a continuous r.v. X is given by
f (x) = `1/ (2a)` , for 0 < x < 2a and = 0, otherwise. Show that `P [X < a/ 2] = P [X >( 3a)/ 2]` .
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 class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. If X denotes the age of a randomly selected student, find the probability distribution of X. Find the mean and variance of X.
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 X > 1
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 odd.
Solve the following problem :
A computer installation has 3 terminals. The probability that any one terminal requires attention during a week is 0.1, independent of other terminals. Find the probabilities that 0
Solve the following problem :
A computer installation has 3 terminals. The probability that any one terminal requires attention during a week is 0.1, independent of other terminals. Find the probabilities that 1 terminal requires attention during a week.
Five numbers x1, x2, x3, x4, x5 are randomly selected from the numbers 1, 2, 3, ......., 18 and are arranged in the increasing order such that x1 < x2 < x3 < x4 < x5. What is the probability that x2 = 7 and x4 = 11?
Kiran plays a game of throwing a fair die 3 times but to quit as and when she gets a six. Kiran gets +1 point for a six and –1 for any other number.
- If X denotes the random variable “points earned” then what are the possible values X can take?
- Find the probability distribution of this random variable X.
- Find the expected value of the points she gets.