If X∼N(μ,σ2)X \sim N(\mu, \sigma^2)X∼N(μ,σ2), what is the distribution of Y=aX+bY = aX + bY=aX+b where a≠0a \neq 0a=0?
N(aμ+b,a2σ2)N(a\mu + b, a^2\sigma^2)N(aμ+b,a2σ2)
N(aμ+b,aσ2)N(a\mu + b, a\sigma^2)N(aμ+b,aσ2)
N(μ+b,a2σ2)N(\mu + b, a^2\sigma^2)N(μ+b,a2σ2)
N(aμ,a2σ2)N(a\mu, a^2\sigma^2)N(aμ,a2σ2)