Answer to Question #321122 in Statistics and Probability for Konjo

Question #321122

The probability density function of a continuous random variable X is given below:



𝑓(π‘₯) = {



1.25(1 βˆ’ π‘₯



4



) , 0 < π‘₯ < 1



0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’



a. Find P(0.4< X<0.9)



b. Compute the expected value and variance of X.

1
Expert's answer
2022-04-03T15:10:58-0400

a:P(0.4<X<0.9)=∫0.40.91.25(1βˆ’x4)dx=1.25(0.5βˆ’0.95βˆ’0.455)=0.479938b:EX=∫01xβ‹…1.25(1βˆ’x4)dx=1.25(12βˆ’16)=0.416667EX2=∫01x2β‹…1.25(1βˆ’x4)dx=1.25(13βˆ’17)=0.238095Var(X)=0.238095βˆ’0.4166672=0.0644836a:\\P\left( 0.4<X<0.9 \right) =\int_{0.4}^{0.9}{1.25\left( 1-x^4 \right) dx}=1.25\left( 0.5-\frac{0.9^5-0.4^5}{5} \right) =0.479938\\b:\\EX=\int_0^1{x\cdot 1.25\left( 1-x^4 \right) dx}=1.25\left( \frac{1}{2}-\frac{1}{6} \right) =0.416667\\EX^2=\int_0^1{x^2\cdot 1.25\left( 1-x^4 \right) dx}=1.25\left( \frac{1}{3}-\frac{1}{7} \right) =0.238095\\Var\left( X \right) =0.238095-0.416667^2=0.0644836


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment