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Choose the correct alternative: Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with Probability 0.5. Assume that the results of the flips

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Choose the correct alternative:

Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with Probability 0.5. Assume that the results of the flips are independent and let X equal the total number of heads that result. The value of E[X] is

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Probability Distributions - Exercise 11.6 [पृष्ठ २१९]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 11 Probability Distributions
Exercise 11.6 | Q 9 | पृष्ठ २१९

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 and = 0 otherwise.

P (–0·5 < x or x > 0·5)


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


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)


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).


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 probability that X is between 1 and 3..


F(x) is c.d.f. of discrete r.v. X whose p.m.f. is given by P(x) = `"k"^4C_x` , for x = 0, 1, 2, 3, 4 and P(x) = 0 otherwise then F(5) = _______


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.

Twelve of 20 white rats available for an experiment are male. A scientist randomly selects 5 rats and counts the number of female rats among them.


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


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 P(4 ≤ X < 10)


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 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 P(X > 3)


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)


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) = ?


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 ______ 


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 probability function of a random variable X is defined by P(X = k) = a`((k + 1)/2^k)` for k - 0, 1, 2, 3, 4, 5, then the probability that X takes a prime value is ______


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


Two coins are tossed. Then the probability distribution of number of tails 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) = ______ 


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.


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 ______.


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