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# Probability, Cumulative Distribution Function

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Let X be a random variable with probability density
f(x) = c(1-x^2), if -1<x<1
= 0, if otherwise

Determine the value of the constant , and find the cumulative distribution function of X

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## Probability : Acceptable Range of Values and Cumulative Distribution Function

1) A manufacturer of flashlight batteries wishes to control the quality of its product by rejecting any lot in which the proportion of batteries having unacceptable voltage appears to be too high. To this end, out of each large lot (10,000 batteries), 25 will be selected and tested. If at least 5 of these generate an unacceptable voltage, the entire lot will be rejected. What is the probability that a lot will be rejected if...
a) 5% of the batteries in the lot have unacceptable voltages?
b) 10% of the batteries in the lot have unacceptable voltage?
c) 20% of the batteries in the lot have unacceptable voltage?

2) The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with pdf {see attachment}

a) Compute the cdf of x
b) Obtain an expression for the (100p)th percentile. What is the value for m??
c) Compute E(x) and V(x)
d) If 1.5 thousand gallons are in stock at the beginning of the week and no new supply is due during the week, how much of the 1.5 thousand gallons is expected to be left at the end of the week?

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