English
Tamil Nadu Board of Secondary EducationHSC Science Class 12

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) = 17. Then the value of k is

Advertisements
Advertisements

Question

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

Options

  • 1

  • 2

  • 3

  • 4

MCQ
Advertisements

Solution

2

shaalaa.com
  Is there an error in this question or solution?
Chapter 11: Probability Distributions - Exercise 11.6 [Page 220]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 11 Probability Distributions
Exercise 11.6 | Q 14 | Page 220

RELATED QUESTIONS

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)


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(1 < x < 2)


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 > 0)


Choose the correct option from the given alternative:

If the a d.r.v. X has the following probability distribution:

X 1 2 3 4 5 6 7
P(X=x) k 2k 2k 3k k2 2k2 7k2+k

k = 


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).


Fill in the blank :

The values of discrete 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.

Amount of syrup prescribed by a physician.


c.d.f. of a discrete random variable X 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 probability mass function


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


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 P(X ≥ 6)


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 the value of k


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 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)


If Xis a.r.v. with c.d.f F (x) and its probability distribution is given by

X = x - 1.5 -0.5 0.5 1.5 2.5
P(X = x) 0.05 0.2 0.15 0.25 0.35

then, F(1.5) - F(- 0.5) = ?


Choose the correct alternative:

A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 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:


Let X = time (in minutes) that lapses between the ringing of the bell at the end of a lecture and the actual time when the professor ends the lecture. Suppose X has p.d.f.

f(x) = `{(kx^2","      0 ≤ x ≤ 2), (0","         "othenwise"):}`

Then, the probability that the lecture ends within 1 minute of the bell ringing is ______


A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour is ______.


If A = {x ∈ R : x2 - 5 |x| + 6 = 0}, then n(A) = _____.


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 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 ______ 


A random variable X has the following probability distribution:

X = xi 1 2 3 4
P(X = xi) 0.2 0.15 0.3 0.35

The mean and the variance are respectively ______.


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) = ______.


At random variable X – B(n, p), if values of mean and variance of X are 18 and 12 respectively, then total number of possible values of X are ______.


For the following distribution function F(x) of a rv.x.

x 1 2 3 4 5 6
F(x) 0.2 0.37 0.48 0.62 0.85 1

P(3 < x < 5) =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×