2. (a) The following is a two-parameter gamma density function: f(x;a, B) = where a >0,B >0,x. Determine expressions in terms of a and ß for (i) E[X] (m) var(x) (6) Research conducted on the cleanliness of home environments and children yielded the following data in the table below : Condition of home Clean Dirty Condition of child Clean 72 48 Fairly clean 78 22 Dirty 35 45 (i) Calculate expected frequencies for the various cells. (m) Test the hypothesis that there is a gap between the two conditions of cleanliness at 5% level of significance.
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!
![2. (a) The following is a two-parameter gamma density function:
a- -
fixα, β)
I(a)
where a >0,B >0,x20.
Petermine expressions in terms of a and ß for (i) E[X] (i) var(x)
(b) Research conducted on the cleanliness of home environments and children yielded
the
following data in the table below :
Condition of home
Clean
Dirty
Condition of child
Clean
72
48
Fairly clean
78
22
Dirty
35
45
(i) Calculate expected frequencies for the various cells.
(m) Test the hypothesis that there is a gap between the two conditions of cleanliness at 5%
level
of significance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03819c4a-d870-4128-b36b-89fdefaa8556%2F3c0699f5-ef04-489e-af1c-2a3245ddefbd%2Fsdyigc_processed.png&w=3840&q=75)
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