Suppose that for a certain brand of battery, the life in months is exponentially distributed with a deca parameter of m = 77 In symbols, we say that the random variable X ~ E(m), where in this case 1 m = 77 a. What is the expected battery life?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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1
. In symbols, we say that the random variable X~ E(m), where in this case
77
parameter of m =
1
m =
77
a. What is the expected battery life?
Expected value is the mean, pu = -
m
Online
Expected life (in months) is
e
b. What is the standard deviation in ages?
The formula is o = ju.
cover
Standard deviation (in months) is
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let
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c. Find the probability that a battery lasts less than c = 71 months. Round to three decimals.
The formula is P(X < x) = 1 - emz.
P(X < 71) =
d. What is the 80th percentile for battery life? Round the percent to one decimal.
We want the value c for which P(X < c) = 0.8, so 1 - e = 0.8.
The 80th percentile is
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Round to one decimal.
We want to find P(X > 83), and then multiply by the number of batteries in the sample.
The expected number of batteries is
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