मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Solve the following : Identify the random variable as either discrete or continuous in each of the following. Write down the range of it. 20 white rats are available for an experiment. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Solve the following :

Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

20 white rats are available for an experiment. Twelve rats are male. Scientist randomly selects 5 rats number of female rats selected on a specific day

बेरीज
Advertisements

उत्तर

Let X = number of female rats selected on a specific day

Since the total number of rats is 20 which include 12 males and 8 females, X takes the finite values

∴ random variable X is discrete.

Range = {0, 1, 2, 3, 4, 5}

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Probability Distributions - Miscellaneous Exercise 2 [पृष्ठ २४२]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 7 Probability Distributions
Miscellaneous Exercise 2 | Q 1.4 | पृष्ठ २४२

संबंधित प्रश्‍न

Find the probability distribution of number of heads in four tosses of a coin.


The random variable X has probability distribution P(X) of the following form, where k is some number:

`P(X = x) {(k, if x = 0),(2k, if x = 1),(3k, if x = 2),(0, "otherwise"):}`

  1. Determine the value of 'k'.
  2. Find P(X < 2), P(X ≥ 2), P(X ≤ 2).

Assume that the chances of the patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?


If the probability that a fluorescent light has a useful life of at least 800 hours is 0.9, find the probabilities that among 20 such lights at least 2 will not have a useful life of at least 800 hours. [Given : (0⋅9)19 = 0⋅1348]

 


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.


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.


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


Find the probability distribution of the number of heads, when three coins are tossed. 


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.


A fair die is tossed twice. If the number appearing on the top is less than 3, it is a success. Find the probability distribution of number of successes.


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.


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 fair coin is tossed four times. Let X denote the number of heads occurring. Find the probability distribution, mean and variance of X.


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.


For what value of k the following distribution is a probability distribution?

X = xi : 0 1 2 3
P (X = xi) : 2k4 3k2 − 5k3 2k − 3k2 3k − 1

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


A random variable has the following probability distribution:

X = xi : 0 1 2 3 4 5 6 7
P (X = xi) : 0 2 p 2 p  3 p  p2 p2 p2 2 p 

The value of p is


From a lot of 15 bulbs which include 5 defective, 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.     


Write the negation of the following statements : 

(a) Chetan has black hair and blue eyes. 
(b) ∃ x ∈ R such that x2 + 3 > 0. 


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 


The defects on a plywood sheet occur at random with an average of the defect per 50 sq. ft. What Is the probability that such sheet will have-

(a) No defects
(b) At least one defect 
[Use e-1 = 0.3678]


Determine whether each of the following is a probability distribution. Give reasons for your answer.

x 0 1 2 3 4
P(x) 0.1 0.5 0.2 –0.1 0.3

Determine whether each of the following is a probability distribution. Give reasons for your answer.

z 3 2 1 0 -1
P(z) 0.3 0.2 0.4. 0.05 0.05

Determine whether each of the following is a probability distribution. Give reasons for your answer.

x 0 1 2
P(x) 0.3 0.4 0.2

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.


In a multiple choice test with three possible answers for each of the five questions, what is the probability of a candidate getting four or more correct answers by random choice?


Find the probability of throwing at most 2 sixes in 6 throws of a single die.


Defects on plywood sheet occur at random with the average of one defect per 50 sq.ft. Find the probability that such a sheet has:

  1. no defect
  2. at least one defect
    Use e−1 = 0.3678

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


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 :

If a fair coin is tossed 4 times, find the probability that it shows head in the first 2 tosses and tail in last 2 tosses.


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 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 :

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.


Solve the following problem :

In a large school, 80% of the students like mathematics. A visitor asks each of 4 students, selected at random, whether they like mathematics.

Calculate the probabilities of obtaining an answer yes from all of the selected students.


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 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 ______


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)`


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.


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 P(X ≤ 2) and P(X > 2)


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`

Find P(X ≤ 2) + P (X > 2)


Two probability distributions of the discrete random variable X and Y are given below.

X 0 1 2 3
P(X) `1/5` `2/5` `1/5` `1/5`

 

Y 0 1 2 3
P(Y) `1/5` `3/10` `2/10` `1/10`

Prove that E(Y2) = 2E(X).


The probability distribution of a discrete random variable X is given below:

X 2 3 4 5
P(X) `5/"k"` `7/"k"` `9/"k"` `11/"k"`

The value of k is ______.


Find the mean of number randomly selected from 1 to 15.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×