Homework Problem H5: This problem combined with Homework Problem H4 makes some key comparisons between Chapters 6 and 7. a) Verify that the function f(x) = 1 with its domain being the interval [5,10] is a valid p.d.f. of a continuous random variable X. Note: this is the function you graphed in homework exercise 18 in section 7.1. b) Consider the funiction f(x) = with the domain being the interval 5/27 (-00, 00) (you do not need to memorize this formula). This function is called the normal probability density function with mean 11 and standard deviation 5. It can be verified that this function is a valid of a random variable X. c) Using the function from part a) above, compute P(X = 7). d) Using the function from part a) above, compute P(X 27). e) General Rule for finding P(as X

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Homework Problem H5: This problem combined with Homework Problem H4 makes
some key comparisons between Chapters 6 and 7.
a) Verify that the function f(x):
with its domain being the interval [5,10] is a
!!
valid p.d.f. of a continuous random variable X. Note: this is the function you
graphed in homework exercise 18 in section 7.1.
b) Consider the funiction f(x) =
with the domain being the interval
5/27
(-0, 00) (you do not need to memorize this formula). This fumction is called the
normal probability density function with mean 11 and standard deviation 5. It can
be verified that this function is a valid
of a
random variable X.
c) Using the function from part a) above, compute P(X = 7).
d) Using the function from part a) above, compute P(X 27).
e) General Rule for finding P(asX <b) in all cases when X is continuous (as
opposed to being discrete): If f is a probability density function (p.d.f.) of a
continuous random variable X, then P(asX sb) is found by computing the
to
of f from
under the
Transcribed Image Text:Homework Problem H5: This problem combined with Homework Problem H4 makes some key comparisons between Chapters 6 and 7. a) Verify that the function f(x): with its domain being the interval [5,10] is a !! valid p.d.f. of a continuous random variable X. Note: this is the function you graphed in homework exercise 18 in section 7.1. b) Consider the funiction f(x) = with the domain being the interval 5/27 (-0, 00) (you do not need to memorize this formula). This fumction is called the normal probability density function with mean 11 and standard deviation 5. It can be verified that this function is a valid of a random variable X. c) Using the function from part a) above, compute P(X = 7). d) Using the function from part a) above, compute P(X 27). e) General Rule for finding P(asX <b) in all cases when X is continuous (as opposed to being discrete): If f is a probability density function (p.d.f.) of a continuous random variable X, then P(asX sb) is found by computing the to of f from under the
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