Question

10. Let X be a random variable with probability distribution function f (x)=0.2 for 1x/<1 = 0.1 for 1 < x < 4 = 0
otherwise The probability P (0.5 < x < 5) is
A.0.3
B.0.5
C.0.4
D. 0.8​

Answer 1

Q) Let X be a random variable with probability distribution function

f (x)=0.2 for 1x/<1 = 0.1 for 1 < x < 4 = 0

otherwise The probability P (0.5 < x < 5)

The probability P (0.5 < x < 5) is _____

a) 0.3

b) 0.5

c) 0.4

d) 0.8

Option(C) 0.4 is the answer.

Given,

Probability distribution function f(x) = $\left \{ {{0.2, for|x|\leq1 } \atop {0.1, for 1\leq |x|\leq 4}\right$, 0, otherwise.

To Find,

The probability P(0.5< x <5)

Solution,

From the given probability distribution function,

f(x) = 0.2, when value of x $\leq 1$

f(x) = 0.1, when 1 $\leq x\leq 4$

f(x) = 0, otherwise.

f(x) = 0.2, when x = (-1,1).

f(x) = 0.1, when x = ( -4, -1) ∪ ((1, 4)

f(x) = 0

Given probability is P(0.5<x<5),

(P) = $\int\limits^\alpha _{-\alpha} {f(x)} \, dx$

(P) = $\int\limits^1_{.5} {0.2} \, dx + \int\limits^4_1 {0.1} \, dx$

0.2[ 1 - 0.5] + 0.1 [ 4 - 1]

P = 0.1 × 0.5 + 0.1 × 3

P = 0.1 + 0.3

P = 0.4.

Hence, 0.4 is the probability of P ( 0.5 < x < 5).

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