ผลต่างระหว่างรุ่นของ "Probstat/homework 2"

รุ่นแก้ไขเมื่อ 15:43, 29 พฤศจิกายน 2557

This is part of [probstat]].

Deadline: December 7th, 2014.

Part 1: Review of the normal distributions.

work on Week 8 practice 2, basic practice, questions 2,4,6,8, and 10.

Part 2: Distribution of sample means.

2.1 Consider a discrete random variable $Y$ where $P\{Y=0\}=0.3$ , $P\{Y=1\}=0.3$ , and $P\{Y=2\}=0.4$ .

(a) If we take a sample of size 2, and let ${\bar {Y}}$ be the sample mean. Describe the distribution of ${\bar {Y}}$ .

(b) If we take a sample of size 3, and let ${\bar {Y}}$ be the sample mean. Describe the distribution of ${\bar {Y}}$ .

2.2 Suppose that the population is normally distributed with mean $\mu =10$ and variance $\sigma ^{2}=4$ . Let ${\bar {X}}$ be the mean of a sample of size 10. Describe the distribution of ${\bar {X}}$ .

2.3 Find $P\{{\bar {X}}>11\}$ . (Hint: use the standard normal table to find the answer.)

2.4 Find $P\{|{\bar {X}}-10|>1\}$ . (Hint: use the standard normal table to find the answer.)

@@ แถว 9: / แถว 9: @@
 == Part 2: Distribution of sample means. ==
-.1 Suppose that the population is normally distributed with mean <math>\mu=10</math> and variance <math>\sigma^2 = 4</math>.  Let <math>\bar{X}</math> be the mean of  a sample of size 10. Describe the distribution of <math>\bar{X}</math>.
+.1 Consider a discrete random variable <math>Y</math> where <math>P\{Y=0\} = 0.3</math>, <math>P\{Y=1\} = 0.3</math>, and <math>P\{Y=2\} = 0.4</math>.
-.2 Find <math>P\{\bar{X} > 11\}</math>.  (Hint: use the standard normal table to find the answer.)
+(a) If we take a sample of size 2, and let <math>\bar{Y}</math> be the sample mean.  Describe the distribution of <math>\bar{Y}</math>.
-.3 Find <math>P\{|\bar{X} - 10 | > 1\}</math>.  (Hint: use the standard normal table to find the answer.)
+(b) If we take a sample of size 3, and let <math>\bar{Y}</math> be the sample mean.  Describe the distribution of <math>\bar{Y}</math>.
-.4 Consider a discrete random variable <math>Y</math> where <math>P\{Y=0\} = 0.3</math>, <math>P\{Y=1\} = 0.3</math>, and <math>P\{Y=2\} = 0.4</math>.
+.2 Suppose that the population is normally distributed with mean <math>\mu=10</math> and variance <math>\sigma^2 = 4</math>.  Let <math>\bar{X}</math> be the mean of  a sample of size 10. Describe the distribution of <math>\bar{X}</math>.
-(a) If we take a sample of size 2, and let <math>\bar{Y}</math> be the sample mean.  Describe the distribution of <math>\bar{Y}</math>.
+.3 Find <math>P\{\bar{X} > 11\}</math>.  (Hint: use the standard normal table to find the answer.)
-(b) If we take a sample of size 3, and let <math>\bar{Y}</math> be the sample mean.  Describe the distribution of <math>\bar{Y}</math>.
+.4 Find <math>P\{|\bar{X} - 10 | > 1\}</math>.  (Hint: use the standard normal table to find the answer.)
 == Part 3: Estimations and confidence intervals. ==

ผลต่างระหว่างรุ่นของ "Probstat/homework 2"

รุ่นแก้ไขเมื่อ 15:43, 29 พฤศจิกายน 2557

Part 1: Review of the normal distributions.

Part 2: Distribution of sample means.

Part 3: Estimations and confidence intervals.

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