A dealer's profit, in units of $2000, on a new automobile is a random variable X having the density function below. Complete parts (a) through (c) below. f(x) = 2 15(4-x), 0≤x≤3, 0, elsewhere (a) Find the variance of the dealer's profit. $ 2640000 (Type an integer or a decimal. Round to the nearest dollar as needed.) (b) Demonstrate that Chebyshev's theorem holds for k=1.88 with the provided density function. For k=1.88, Chebyshev's theorem states that P(. Chebyshev's theorem k = 1.88, since the probability is equal to (Type integers or decimals. Round to four decimal places as needed.) for

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c) what is the probability that the profit exceeds 1200$

A dealer's profit, in units of $2000, on a new automobile is a random variable X having the density function below.
Complete parts (a) through (c) below.
f(x) =
2
15(4-x), 0≤x≤3,
elsewhere
0,
(a) Find the variance of the dealer's profit.
$2640000
(Type an integer or a decimal. Round to the nearest dollar as needed.)
(b) Demonstrate that Chebyshev's theorem holds for k=1.88 with the provided density function.
For k=1.88, Chebyshev's theorem states that P(< X<². Chebyshev's theorem
k = 1.88, since the probability is equal to
(Type integers or decimals. Round to four decimal places as needed.)
for
Transcribed Image Text:A dealer's profit, in units of $2000, on a new automobile is a random variable X having the density function below. Complete parts (a) through (c) below. f(x) = 2 15(4-x), 0≤x≤3, elsewhere 0, (a) Find the variance of the dealer's profit. $2640000 (Type an integer or a decimal. Round to the nearest dollar as needed.) (b) Demonstrate that Chebyshev's theorem holds for k=1.88 with the provided density function. For k=1.88, Chebyshev's theorem states that P(< X<². Chebyshev's theorem k = 1.88, since the probability is equal to (Type integers or decimals. Round to four decimal places as needed.) for
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