1. Find the mean, standard deviation, and variance X P(x) 1 0.23 2 0.38 3. 0.31

Question

1. Find the mean, standard deviation, and variance X P(x) 1 0.23 2 0.38 3. 0.31 4 0.08 2. A company tests five clocks. There is a.04 rate of defects. Find a) the mean number of defects b) the variance for the number of defects c) the standard deviation for the number of defects per batch d) the probability of getting exactly 3 defects in batch In a game of chance, there is an 15% probability of winning $70, a 5% probability of winning $20, and a 80% probability of $10. Find the expected value if it costs $30 to play 3

Explanation / Answer

1) the mean is given by

=(1*0.23)+(2*0.38)+(3*0.31)+(4*0.08)=2.24.

to find the variance , we need to find E(X^2)

E(X^2)=(1^2*0.23)+(2^2*0.38)+(3^2*0.31)+(4^2*0.08)=5.28

var(X)=E(X^2)-(E(X))^2=5.28-2.24^2=0.8024

and standard deviarion is sqrt(var(X))=sqrt(0.8024)=0.895767

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