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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: - Mathematics

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प्रश्न

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:

विकल्प

  • `1/15`

  • `1/10`

  • `1/3`

  • `2/3`

MCQ
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उत्तर

`2/3`

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Types of Random Variables
  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 17 | 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)


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)


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 = 


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 _______


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


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


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 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:

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


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


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 ______


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) = ______ 


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) =


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 ______.


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