The manager of a stockroom in a factory has constructed the following probability distribution for the daily demand (number of times used) for a particular tool Y 0 1 2 P(y) 0.1 0.5 0.4 It costs the factory $10 each time the tool is used. Find the mean and the variance of the daily cost for use of the tool.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The manager of a stockroom in a factory has constructed the following probability
distribution for the daily demand (number of times used) for a particular tool
Y 0 1 2
P(y) 0.1 0.5 0.4
It costs the factory $10 each time the tool is used. Find the mean and the variance of
the daily cost for use of the tool.
(b) A random variable X has a probability density
⎩
⎨
⎧ − ≤ ≤ = otherwise
Ax x x
f x
0,
(6 ) ,0 6
( )
2
(i) Find the value of the constant A
(ii) Calculate E(X) ,
(c) A certain manufacturing process yields electrical fuses of which, in the long run
15% are defective. Find the probability that in a random sample of size n=10, fuses
selected from this process, there will be
(i) No defective fuse
(ii) At least one defective fuse
(iii) Exactly two defective fuses
(iv) At most one defective fuse
(d) The number of errors in a text book follows a Poisson distribution with mean of
0.01 errors per page. What is the probability that there are three or less errors in
100pages?
(e) The random variable X is B(n,0.3) and E(X) =2.4. find n and the standard deviation
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