plifetime: Probability of Battery Lifetime
In austinragotzy/mathstat: Introduction to Mathematical Statistics R Package

Description Usage Arguments Details Value References Examples

Let X & Y be the survival times of two batteries. This functions calculates the probability that (X, Y) falls within the rectangle which represents the distribution of battery lifetime.The modes of the survival time are (x, y) = (sqrt(2)/2, sqrt(2)/2). X and Y denote the lifetimes of the batteries of the component in standard units.

1	plifetime(x1, x2, y1, y2)

`x1`	a continuous vertical line which intersects with lines 'c' and 'd'
`x2`	a continuous vertical line which intersects with lines 'c' and 'd'
`y1`	a continuous horizontal line which intersects with lines 'a' and 'b'
`y2`	a continuous horizontal line which intersects with lines 'a' and 'b'

Below is the function's pdf:

1 2	pdf(x,y) = { 4xye^-(x^2 + y^2), when x > 0, y > 0 { 0 otherwise

This function is used to solve Exercise 2.1.6 on page 98 of the book.

The probability that (X, Y) falls within the rectangle, which is created at the intersections of the the lines 'a', 'b', 'c', and 'd'.

Hogg, R., McKean, J., Craig, A. (2018) Introduction to Mathematical Statistics, 8th Ed. Boston: Pearson.

x1 <- 2
x2 <- 3
y1 <- 2
y2 <- 3

plifetime(x1, x2, y1, y2)

# Probability of (X, Y) surviving beyond the mode lifetime of the batteries
x1 <- 1
x2 <- 2
y1 <- Inf
y2 <- Inf

plifetime(x1, x2, y1, y2)