Gamma distribution
A gamma distribution also falls from the class of distributions with waiting times such as exponential spread. When the gamma form parameter is equal to one, otherwise it is exponential. Using the chi-square function it's simple to measure the probability of gamma variables.
The probability that a transistor will last between 10 and 20 weeks is calculated as follows:
[tex]\begin{aligned}P(10<X<20) &=P(X<20)-P(X<10) \\&=P(2 \lambda X<8)-P(2 \lambda X<4) \\&=P\left(\chi_{8}^{2} \leq 8\right)-P\left(\chi_{8}^{2} \leq 4\right) \\&=0.57-0.14 \\&=0.43\end{aligned}[/tex]
Hence, the probability that a transistor will last between 10 and 20 weeks is 0.43.
