If X ~ Lognormal(mu, sigma^2) and Y = cX, what is the distribution of Y?

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Multiple Choice

If X ~ Lognormal(mu, sigma^2) and Y = cX, what is the distribution of Y?

Scaling a lognormal variable by a positive constant preserves the lognormal form but shifts the log-mean. If X is lognormal with parameters mu and sigma^2, then ln X is Normal(mu, sigma^2). For Y = cX with c > 0, ln Y = ln(cX) = ln c + ln X. Since ln X is Normal(mu, sigma^2), ln Y is Normal(mu + ln c, sigma^2). Therefore Y is lognormal with parameters mu + ln c and sigma^2. (If c ≤ 0, Y is not lognormal.)

Scaling a lognormal variable by a positive constant preserves the lognormal form but shifts the log-mean. If X is lognormal with parameters mu and sigma^2, then ln X is Normal(mu, sigma^2). For Y = cX with c > 0, ln Y = ln(cX) = ln c + ln X. Since ln X is Normal(mu, sigma^2), ln Y is Normal(mu + ln c, sigma^2). Therefore Y is lognormal with parameters mu + ln c and sigma^2. (If c ≤ 0, Y is not lognormal.)

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