Demand The weekly demand x (in tons) for a certain product is described by the probability density function
Find and interpret each probability.
a)
To calculate: The probability for the range
Given Information:
The weekly demand x for a certain product is described by the probability density function,
Formula used:
In a probability density function, the probability that x lies in interval
Which is shown in the figure below,
Integration by parts.
When u and v is assumed to be the differentiable functions of x then,
Calculation:
Consider the exponential probability density function,
In order to calculate the probability for the range
Thus,
In order to solve the integral
Let
Apply integral on both sides of the above equation as,
Thus,
Then differentiate both sides of the equation
Substitute
b)
To calculate: The probability for the range
c)
To calculate: The probability for the range
d)
To calculate: The probability for the range
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