हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा १२

A random variable X has the following probability mass function. x 1 2 3 4 5 F(x) k2 2k2 3k2 2k 3k Find P(2 ≤ X < 5) - Mathematics

Advertisements
Advertisements

प्रश्न

A random variable X has the following probability mass function.

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

Find P(2 ≤ X < 5)

योग

उत्तर

P(2 ≤ X < 5) = P(X = 2) + P(X = 3) + P(X = 4)

= `2/36 + 3/36 + 2/6`

= `(2 + 3 + 12)/36 + 17/36`

shaalaa.com
Types of Random Variables
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Probability Distributions - Exercise 11.2 [पृष्ठ १९४]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 11 Probability Distributions
Exercise 11.2 | Q 6. (ii) | पृष्ठ १९४

संबंधित प्रश्न

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,"),(0                                 "otherwise".):}`

P(–1 < x < 1)


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


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 < 1) 


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. 


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.

Amount of syrup prescribed by a physician.


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.


c.d.f. of a discrete random variable X is


The probability distribution of a r.v. X is

X = x -3 -2 -1 0 1
P(X = x) 0.3 0.2 0.25 0.1 0.15

Then F (-1) = ?


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


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)


Choose the correct alternative:

Suppose that X takes on one of the values 0, 1 and 2. If for some constant k, P(X = i) = kP(X = i – 1) for i = 1, 2 and P(X = 0) = `1/7`. Then the value of k is


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 ______ 


X is a continuous random variable with a probability density function

f(x) = `{{:(x^2/4 + k;     0 ≤ x ≤ 2),(0;              "otherwise"):}`

The value of k is equal to ______


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 = x -4 -2 -1 0 2 4 6 8
F(x) 0.2 0.4 0.55 0.6 0.75 0.80 0.95 1

Then P(X ≤ 4|X > -1) = ?


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×