4. The continuous random variable X has a lognormal distribution if the random variable Y = In(X) has a normal distribution with mean and variance o². Let X₁...., X20 be a random sample from a lognormal distribution with unknown parameters and o². If the sample values are: 5.75 5.73 5.57 5.86 5.28 5.26 (a) (b) 5.67 5.42 6.02 5.85 5.39 5.50 5.37 5.34 5.66 6.13 5.79 6.04 6.07 5.64 What is the value of the unbiased estimate of ? What is the value of the maximum likelihood estimate of μ? (c) What is the value of the unbiased estimate of o²? (d) What is the value of the maximum likelihood estimate of o²?

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4. The continuous random variable X has a lognormal distribution if the random variable Y = ln(X)
has a normal distribution with mean and variance o². Let X₁..., X20 be a random sample from a
lognormal distribution with unknown parameters and o2. If the sample values are:
μ
(a)
(b)
5.75
5.86
5.73
5.57
5.28 5.26
5.67 5.42 6.02
5.34 5.66 6.13
5.85 5.39 5.50
5.79
6.04 6.07
What is the value of the unbiased estimate of μ?
What is the value of the maximum likelihood estimate of μ?
(c) What is the value of the unbiased estimate of o2?
(d)
What is the value of the maximum likelihood estimate of o²?
5.37
5.64
Transcribed Image Text:4. The continuous random variable X has a lognormal distribution if the random variable Y = ln(X) has a normal distribution with mean and variance o². Let X₁..., X20 be a random sample from a lognormal distribution with unknown parameters and o2. If the sample values are: μ (a) (b) 5.75 5.86 5.73 5.57 5.28 5.26 5.67 5.42 6.02 5.34 5.66 6.13 5.85 5.39 5.50 5.79 6.04 6.07 What is the value of the unbiased estimate of μ? What is the value of the maximum likelihood estimate of μ? (c) What is the value of the unbiased estimate of o2? (d) What is the value of the maximum likelihood estimate of o²? 5.37 5.64
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