The moment generating function (MGF) of a standard normal distribution is given by M(t) = e^(t^2/2).

When t = 0, we substitute 0 into the equation to get M(0) = e^(0^2/2) = e^0.

Since any number raised to the power of 0 is 1, the MGF of a standard normal distribution at t = 0 is 1.

Question

The moment generating function (MGF) of a standard normal distribution is given by M(t) = e^(t^2/2).

When t = 0, we substitute 0 into the equation to get M(0) = e^(0^2/2) = e^0.

Since any number raised to the power of 0 is 1, the MGF of a standard normal distribution at t = 0 is 1.

Knowee AI · Accepted Answer

The moment generating function (MGF) of a standard normal distribution is given by M(t) = e^(t^2/2).

When t = 0, we substitute 0 into the equation to get M(0) = e^(0^2/2) = e^0.

Since any number raised to the power of 0 is 1, the MGF of a standard normal distribution at t = 0 is 1.

For a standard normal distribution, what is the MGF at t=0?