Suppose X t(4), Y~ t(200), and Z~ N(0, 1). Answer the following questions. Attach R code if used. (a) Compute P(X > 2), P(Y > 2), and P(Z > 2). (b) Compare and contrast the probabilities you got in part (a). Which one has largest probability? Which one has the smallest probability? Which ones are close to each other? Which ones are different from each other? (c) Compute P(-0.5 < X < 0.5), P(-0.5

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Suppose X t(4), Y t(200), and Z~ N(0, 1). Answer the following
questions. Attach R code if used.
(a) Compute P(X > 2), P(Y > 2), and P(Z > 2).
(b) Compare and contrast the probabilities you got in part (a). Which one has largest
probability? Which one has the smallest probability? Which ones are close to each
other? Which ones are different from each other?
(c) Compute P(-0.5 < X < 0.5), P(-0.5<Y <0.5), and P(-0.5 < Z < 0.5).
(c) Compare and contrast the probabilities you got in part (c). Which one has largest
probability? Which one has the smallest probability? Which ones are close to each
other? Which ones are different from each other?
(e) Based on your answers in the previous parts, complete the following sentence.
"Compared with the standard normal distribution and the t-distribution with a
large degrees of freedom, the t-distribution with a small degrees of freedom has
cails and
center."
Transcribed Image Text:Suppose X t(4), Y t(200), and Z~ N(0, 1). Answer the following questions. Attach R code if used. (a) Compute P(X > 2), P(Y > 2), and P(Z > 2). (b) Compare and contrast the probabilities you got in part (a). Which one has largest probability? Which one has the smallest probability? Which ones are close to each other? Which ones are different from each other? (c) Compute P(-0.5 < X < 0.5), P(-0.5<Y <0.5), and P(-0.5 < Z < 0.5). (c) Compare and contrast the probabilities you got in part (c). Which one has largest probability? Which one has the smallest probability? Which ones are close to each other? Which ones are different from each other? (e) Based on your answers in the previous parts, complete the following sentence. "Compared with the standard normal distribution and the t-distribution with a large degrees of freedom, the t-distribution with a small degrees of freedom has cails and center."
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