हिंदी

Solve the following problem : Following is the probability distribution of a r.v.X.Find the probability that X is non-negative - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

योग

उत्तर

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

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Probability Distributions - Part I [पृष्ठ १५५]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Commerce) [English] 12 Standard HSC Maharashtra State Board
अध्याय 8 Probability Distributions
Part I | Q 1.03 | पृष्ठ १५५

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


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


Which of the following distributions of probabilities of a random variable X are the probability distributions?
(i)

X : 3 2 1 0 −1
(X) : 0.3 0.2 0.4 0.1 0.05
 
(ii)
X : 0 1 2
P (X) : 0.6 0.4 0.2


(iii)

X : 0 1 2 3 4
P (X) : 0.1 0.5 0.2 0.1 0.1
 


(iv)

X : 0 1 2 3
P (X) : 0.3 0.2 0.4 0.1
 

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


Four cards are drawn simultaneously from a well shuffled pack of 52 playing cards. Find the probability distribution of the number of aces.


A bag contains 4 red and 6 black balls. Three balls are drawn at random. Find the probability distribution of the number of red balls.


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 cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of kings.


Two cards are drawn successively without replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces.


An urn contains 4 red and 3 blue balls. Find the probability distribution of the number of blue balls in a random draw of 3 balls with replacement.


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 the value of k .


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) .


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

x 0 1 2 3
P(X) k
\[\frac{k}{2}\]
\[\frac{k}{4}\]
\[\frac{k}{8}\]

 Find P(X ≤ 2) + P(X > 2) .

 

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 : -5 -4 1 2
pi : \[\frac{1}{4}\] \[\frac{1}{8}\] \[\frac{1}{2}\] \[\frac{1}{8}\]
 

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.


Using the truth table verify that p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r).


If the demand function is D = 150 - p2 - 3p, find marginal revenue, average revenue and elasticity of demand for price p = 3. 


A fair coin is tossed 12 times. Find the probability of getting exactly 7 heads .


If X ∼ N (4,25), then find P(x ≤ 4)


The p.d.f. of r.v. of X is given by

f (x) = `k /sqrtx` , for 0 < x < 4 and = 0, otherwise. Determine k .

Determine c.d.f. of X and hence P (X ≤ 2) and P(X ≤ 1).


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

x 0 1 2
P(x) 0.4 0.4 0.2

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

y –1 0 1
P(y) 0.6 0.1 0.2

A die is thrown 4 times. If ‘getting an odd number’ is a success, find the probability of 2 successes


A die is thrown 4 times. If ‘getting an odd number’ is a success, find the probability of at least 3 successes


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.


Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as six appears on at least one die


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.


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(3X2)


If the p.m.f of a r. v. X is

P(x) = `c/x^3`, for x = 1, 2, 3

        = 0, otherwise

then E(X) = ______.


Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a nonprime number. The probability that the card was drawn from Box I is ______.


A person throws two fair dice. He wins ₹ 15 for throwing a doublet (same numbers on the two dice), wins ₹ 12 when the throw results in the sum of 9, and loses ₹ 6 for any other outcome on the throw. Then the expected gain/loss (in ₹) of the person is ______.


Two balls are drawn at random one by one with replacement from an urn containing equal number of red balls and green balls. Find the probability distribution of number of red balls. Also, find the mean of the random variable.


Two numbers are selected from first six even natural numbers at random without replacement. If X denotes the greater of two numbers selected, find the probability distribution of X.


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?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×