The probability density function of X is f(x)=\frac{1}{10} for 0 \leq x \leq 10. Then P(X+ \frac{10}{X} \geq 7) is?

UkusakazaL

UkusakazaL

Answered question

2021-08-06

The probability density function of X is f(x)=110 for 0x10. Then P(X+10X7) is:

Answer & Explanation

beljuA

beljuA

Beginner2021-08-09Added 2 answers

Step 1
The probability density function is given as,
f(x)=110 for 0x10.
To determine the value of the probability,P(X+10X7).
P(X+10X7)=P(X2+107X)
P(X27X+100)
P(0X2orX5).
Step 2
Solve the probability function for the above intervals,
At 0X2,
P(0X2)=02f(x)dx
=11002dx.
=110[x]02
=110×2
=15
Step 3
At X5,
P(x5)=510f(x)dx
=110510dx.
=110[x]510
=110×(105)
=110×5
=12
Step 4
Thus , the value of the P(X+10X7) is,
P(X+10X7)=P(0X2orX5)
=15+12
=710
=0.7

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