English

The following is the p.d.f. of continuous r.v. f (x) = x8 , for 0 < x < 4 and = 0 otherwise. Find F(x) at x = 0·5 , 1.7 and 5 - Mathematics and Statistics

Advertisements
Advertisements

Question

The following is the p.d.f. of continuous r.v.

f (x) = `x/8` , for 0 < x < 4 and = 0 otherwise.

Find F(x) at x = 0·5 , 1.7 and 5

Sum
Advertisements

Solution

F(0.5) =`F(1/2) = (1/2)^2/16 = 1/64`

F(1.7) = `(1.7)^2/16 = 2.89/16 = 0.18`

f (x) = `x/8` , for 0 < x < 4 and 5 > 4

∴ F(5) = 1.

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Probability Distributions - Exercise 7.2 [Page 239]

APPEARS IN

RELATED QUESTIONS

Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f.

f (x) = k `(4 – x^2 )`, for –2 ≤ x ≤ 2 and = 0 otherwise.

P(x > 0)


Given the p.d.f. of a continuous r.v. X ,

f (x) = `x^2 /3` , for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find P( x < –2)


Solve the following :

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

An economist is interested the number of unemployed graduate in the town of population 1 lakh.


The p.m.f. of a r.v. X is given by P (X = x) =`("" ^5 C_x ) /2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise.

Then show that P (X ≤ 2) = P (X ≥ 3).


In the p.m.f. of r.v. X

X 1 2 3 4 5
P (X) `1/20` `3/20` a 2a `1/20`

Find a and obtain c.d.f. of X. 


It is felt that error in measurement of reaction temperature (in celsius) in an experiment is a continuous r.v. with p.d.f.

f(x) = `{(x^3/(64),  "for"  0 ≤ x ≤ 4),(0,   "otherwise."):}`
Verify whether f(x) is a p.d.f.


It is felt that error in measurement of reaction temperature (in celsius) in an experiment is a continuous r.v. with p.d.f.

f(x) = `{(x^3/(64),  "for"  0 ≤ x ≤ 4),(0,   "otherwise."):}`
Find P(0 < X ≤ 1).


It is felt that error in measurement of reaction temperature (in celsius) in an experiment is a continuous r.v. with p.d.f.

f(x) = `{(x^3/(64),  "for"  0 ≤ x ≤ 4),(0,   "otherwise."):}`
Find probability that X is between 1 and 3..


Fill in the blank :

The value of continuous r.v. are generally obtained by _______


Solve the following problem :

Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.

An economist is interested in knowing the number of unemployed graduates in the town with a population of 1 lakh.


Solve the following problem :

Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.

A person on high protein diet is interested in the weight gained in a week.


Solve the following problem :

Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.

A highway safety group is interested in the speed (km/hrs) of a car at a check point.


A coin is tossed 10 times. The probability of getting exactly six heads is ______.


A random variable X has the following probability distribution:

X = x 0 1 2 3
P (X = x) `1/10` `1/2` `1/5` k

Then the value of k is


Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold is ______.


Three fair coins are tossed simultaneously. Find the probability mass function for a number of heads that occurred


A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the cumulative distribution function


Find the probability mass function and cumulative distribution function of a number of girl children in families with 4 children, assuming equal probabilities for boys and girls


Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by 
`f(x) = {{:((x^2 + 1)/k","  "for"  x = 0","  1","  2),(0","  "otherwise"):}` 
Find P(X ≥ 1)


The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0,  - oo < x < - 1),(0.15, - 1 ≤ x < 0),(0.35, 0 ≤ x < 1),(0.60, 1 ≤ x < 2),(0.85, 2 ≤ x < 3),(1, 3 ≤ x < oo):}`
Find the probability mass function


The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0,  - oo < x < - 1),(0.15, - 1 ≤ x < 0),(0.35, 0 ≤ x < 1),(0.60, 1 ≤ x < 2),(0.85, 2 ≤ x < 3),(1, 3 ≤ x < oo):}`
Find P(X ≥ 2)


A random variable X has the following probability mass function.

x 1 2 3 4 5
F(x) k2 2k2 3k2 2k 3k

Find the value of k


The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0,  "for" - oo < x < 0),(1/2,  "for"  0 ≤ x < 1),(3/5,  "for"  1 ≤ x < 2),(4/5,  "for"  2 ≤ x < 4),(9/5,  "for"  3 ≤ x < 4),(1,  "for"   ≤ x < oo):}`
Find the probability mass function


The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0,  "for" - oo < x < 0),(1/2,  "for"  0 ≤ x < 1),(3/5,  "for"  1 ≤ x < 2),(4/5,  "for"  2 ≤ x < 4),(9/5,  "for"  3 ≤ x < 4),(1,  "for"   ≤ x < oo):}`
Find P(X < 3)


Choose the correct alternative:

The probability mass function of a random variable is defined as:

x – 2 – 1 0 1 2
f(x) k 2k 3k 4k 5k

Then E(X ) is equal to:


The p.m.f. of a random variable X is

P(x) = `(5 - x)/10`,   x = 1, 2, 3, 4
       = 0,            otherwise

The value of E(X) is ______ 


If the c.d.f (cumulative distribution function) is given by F(x) = `(x - 25)/10`, then P(27 ≤ x ≤ 33) = ______.


For a random variable X, if Var (X) = 5 and E (X2) = 21, the value of E (X) is ______


A random variable X has the following probability distribution:

X 1 2 3 4
P(X) `1/3` `2/9` `1/3` `1/9`

1hen, the mean of this distribution is ______ 


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

X = k 0 1 2 3 4
P(X = k) 0.1 0.4 0.3 0.2 0

The variance of X is ______


A card is chosen from a well-shuffled pack of cards. The probability of getting an ace of spade or a jack of diamond is ______.


The c.d.f. of a discrete r.v. x is 

x 0 1 2 3 4 5
F(x) 0.16 0.41 0.56 0.70 0.91 1.00

Then P(1 < x ≤ 4) = ______ 


The p.d.f. of a continuous random variable X is

f(x) = 0.1 x, 0 < x < 5

= 0, otherwise

Then the value of P(X > 3) is ______ 


Two cards are randomly drawn, with replacement. from a well shuffled deck of 52 playing cards. Find the probability distribution of the number of aces drawn.


A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) = ______.


If f(x) = `k/2^x` is a probability distribution of a random variable X that can take on the values x = 0, 1, 2, 3, 4. Then, k is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×