2. If x is a value assumed by a random variable X having the exponential distribution given by x > 0, elsewhere f(x) = 0 >0 0 0, Find k so that the interval 0 <0

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
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2. If x is a value assumed by a random variable X having the exponential distribution given by
e e
0
f(x) =
x > 0,
elsewhere
0 > 0
0,
Find k so that the interval 0 <0 <kx is a 1-a confidence interval for the parameter 8.
3. According to the Maxwell-Boltzmann law, the probability density of the speed v of gas molecule is
f(v) = {kv²e-Bv²,
for v > 0
0,
elsewhere
where ß depends on mass and temperature, and k is an appropriate constant. Derive the probability
density g(E) for the kinetic energy E = mv².
Transcribed Image Text:2. If x is a value assumed by a random variable X having the exponential distribution given by e e 0 f(x) = x > 0, elsewhere 0 > 0 0, Find k so that the interval 0 <0 <kx is a 1-a confidence interval for the parameter 8. 3. According to the Maxwell-Boltzmann law, the probability density of the speed v of gas molecule is f(v) = {kv²e-Bv², for v > 0 0, elsewhere where ß depends on mass and temperature, and k is an appropriate constant. Derive the probability density g(E) for the kinetic energy E = mv².
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