(3) is the answer?
The object of a general chemistry experiment is to determine the amount (in milliliters) of sodium hydroxide (NaOH) solution nee
ded to neutralize 1 gram of a specified acid. This will be an exact amount, but when the experiment is run in the laboratory, variation will occur as the result of experimental error. Three titrations are made using phenolphthalein as an indicator of the neutrality of the solution (pH equals 7 for a neutral solution). The three volumes of NaOH required to attain a pH of 7 in each of the three titrations are as follows: 82.00, 75.65, and 75.43 milliliters.
Required:
Use a 99% confidence interval to estimate the mean number of milliliters required to neutralize 1 gram of the acid
Required:
Use a 99% confidence interval to estimate the mean number of milliliters required to neutralize 1 gram of the acid
1 answer:
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Answer:
a. .
b.
Step-by-step explanation:
By the definition, the expected value of a random variable X with probability mass function p is given by where the sum runs over all the posible values of X. Given a function g, the random variable Y=g(X) is defined. Note that the function g induces a probability mass function P' given by P'(Y=k) = P(X=g^{-1}(k)) when the function g is bijective.
a. Note that for 1/3ln(2)+1/6ln(5) by choosing the function g(x) = ln(x) the expression coincides with E(g(x)), because if Y = g(x) then E(Y) = P'(Y=1)*ln(1)+P'(Y=2)*ln(2)+P'(Y=5)*ln(5) = P(X=1)*ln(1)+P(X=2)*ln(2)+P(X=5)*ln(5).
b. On the same fashion, the function g(x) = xe^{xt} fullfills the expression of E[g(X)]