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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

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प्रश्न

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

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Probability Distributions - Exercise 11.6 [पृष्ठ २२०]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 11 Probability Distributions
Exercise 11.6 | Q 14 | पृष्ठ २२०

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 expression for c.d.f. of X


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


Solve the following problem :

A player tosses two coins. He wins ₹ 10 if 2 heads appear, ₹ 5 if 1 head appears, and ₹ 2 if no head appears. Find the expected value and variance of winning amount.


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 _______


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.


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(4 ≤ X < 10)


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


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 < 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 P(X ≥ 2)


Choose the correct alternative:

Which of the following is a discrete random variable?
I. The number of cars crossing a particular signal in a day.
II. The number of customers in a queue to buy train tickets at a moment.
III. The time taken to complete a telephone call.


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


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


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.


Find the probability of getting the sum as a perfect square number when two dice are thrown together.


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