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Solve the following : Identify the random variable as either discrete or continuous in each of the following. Write down the range of it. - Mathematics and Statistics

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प्रश्न

Solve the following :

Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

The person on the high protein diet is interested gain of weight in a week.

योग
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उत्तर

Let X = gain of weight in a week

Then X takes uncountable infinite values

∴ random variable X is continuous.

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अध्याय 7: Probability Distributions - Miscellaneous Exercise 2 [पृष्ठ २४२]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 7 Probability Distributions
Miscellaneous Exercise 2 | Q 1.3 | पृष्ठ २४२

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संबंधित प्रश्न

State if the following is not the probability mass function of a random variable. Give reasons for your answer

Z 3 2 1 0 −1
P(Z) 0.3 0.2 0.4 0 0.05

A random variable X has the following probability distribution:

X 0 1 2 3 4 5 6 7
P(X) 0 k 2k 2k 3k k2 2k2 7k2 + k

Determine:

  1. k
  2. P(X < 3)
  3. P( X > 4)

The following is the p.d.f. of r.v. X :

f(x) = `x/8`, for 0 < x < 4 and = 0 otherwise

P ( 1 < x < 2 )


The following is the p.d.f. of r.v. X:

f(x) = `x/8`, for 0 < x < 4 and = 0 otherwise.

 P(x > 2)


Suppose that X is waiting time in minutes for a bus and its p.d.f. is given by f(x) = `1/5`, for 0 ≤ x ≤ 5 and = 0 otherwise.

Find the probability that waiting time is between 1 and 3.


Choose the correct option from the given alternative:

If a d.r.v. X takes values 0, 1, 2, 3, . . . which probability P (X = x) = k (x + 1)·5 −x , where k is a constant, then P (X = 0) =


Choose the correct option from the given alternative:

If p.m.f. of a d.r.v. X is P (X = x) = `x^2 /(n (n + 1))`, for x = 1, 2, 3, . . ., n and = 0, otherwise then E (X ) =


Choose the correct option from the given alternative :

If p.m.f. of a d.r.v. X is P (x) = `c/ x^3` , for x = 1, 2, 3 and = 0, otherwise (elsewhere) then E (X ) =


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

x -2 -1 0 1 2 3
p(X=x) 0.1 k 0.2 2k 0.3 k

then P (X = −1) =


Choose the correct option from the given alternative:

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x -2 -1 0 1 2 3
p(X=x) 0.1 k 0.2 2k 0.3 k

then P (X = −1) =


Solve the following problem :

A fair coin is tossed 4 times. Let X denote the number of heads obtained. Identify the probability distribution of X and state the formula for p. m. f. of X.


The following is the c.d.f. of r.v. X:

x −3 −2 −1 0 1 2 3 4
F(X) 0.1 0.3 0.5 0.65 0.75 0.85 0.9

1

P (X ≤ 3/ X > 0)


The probability distribution of discrete r.v. X is as follows :

x = x 1 2 3 4 5 6
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f (x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise.

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x 0 1 2
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then E(x) = 2p.


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Find the expected value and variance of the r. v. X if its probability distribution is as follows.

x 1 2 3
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Find the expected value and variance of the r. v. X if its probability distribution is as follows.

x – 1 0 1
P(X = x) `(1)/(5)` `(2)/(5)` `(2)/(5)`

Solve the following problem :

Find the expected value and variance of the r. v. X if its probability distribution is as follows.

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Solve the following problem :

Find the expected value and variance of the r. v. X if its probability distribution is as follows.

X 0 1 2 3 4 5
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Solve the following problem :

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Let X∼B(n,p) If E(X) = 5 and Var(X) = 2.5, find n and p.


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f(x) is c.d.f. of discete r.v. X whose distribution is

xi – 2 – 1 0 1 2
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x 0 1 2
P(x) q2 2pq p2

then Var(x) = ______


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x 1 2 3 4 5 6
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k = `square`


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

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Solution: Since `sum"p"_"i"` = 1

P(X ≤ 4) = `square + square + square + square = square`


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

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= `square - square`

= `square`


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