Let X be the number of test holes required in locating a leak in an underground
ID: 3071654 • Letter: L
Question
Let X be the number of test holes required in locating a leak in an underground natural gas pipeline. Use the probability distribution below to answer the following questions.
(a) Determine the value of x.
(b) Determine the most likely number of test holes that will be drilled.
(c) Determine the probability that fewer than 2 test holes will be drilled.
(d) Determine the expected number of test holes that will be drilled.
(e) Determine E(X2) for the random variable X.
(f) Determine Var(X).
(g) Determine the mean and standard deviation of the random variable 10X 15.
X 1 2 3 4 p(x) 0.5 2x x 0.05Explanation / Answer
Ans:
a)For a valid probability distribution:
0.5+2x+x+0.05=1
0.55+3x=1
3x=0.45
x=0.15
b)Most likely will be which has highest probabilty i.e. x=1
c)P(x<2)=P(x=1)=0.5
d)E(x)=1*0.5+2*0.3+3*0.15+4*0.05=1.75
e)E(x^2)=1^2*0.5+2^2*0.3+3^2*0.15+4^2*0.05=3.85
f)Var(x)=E(x^2)-E(x)^2=3.85-1.75^2=0.7875
g)E(10x-15)=10E(x)-15=10*1.75-15=2.5
SD(10x-15)=10*SD(x)=10*sqrt(0.7875)=8.874
X 1 2 3 4 p(x) 0.5 0.3 0.15 0.05Related Questions
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