Geologists estimate the time since the most recent cooling of a mineral by counting the number of uranium fission tracks on the surface of the mineral. A certain mineral specimen is of such an age that there should be an average of 6 tracks per \(\mathrm{cm}^{2}\) of surface area. Assume the number of tracks in an area follows a Poisson distribution. Let \(X\) represent the number of tracks counted in 1 \(\mathrm{cm}^{2}\) of surface area.

Find

a. P(X = 7)

b. \(P(X \geq 3)\)

c. P(2 < X < 7)

d. \(\mu_{X}\)

e. \(\sigma_{X}\)

Equation Transcription:

Text Transcription:

cm^2

X

P(X geq 3)

mu_X

sigma_X

Solution

Step 1 of 6

Let X represents the no. of tracks

Here X follows poisson distribution with average of 6 tracks

The pmf of poisson distribution is P(X)=, X=0,1,2,..............

Here =6