2 6. Show that a gamma distribution with a > 1 has a relative maximum atx = (a- 1)ß. What happens when 0 < a < 1 and a = 1?%3D

Relative maximum =? For a gamma distribution for alpha>1

Answered: 6. Show that a gamma distribution with…

College Algebra

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ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 5SE: What does the y -intercept on the graph of a logistic equation correspond to for a population...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
3
7. Suppose the distribution of waiting times (in hours) for residents of a particular province trying to book a vaccination appointment is determined by the function 5 5t f (t) ==e¯6, t >0 Find the percentage of residents who wait longer than the mean waiting time. In a sample of 1250 residents, we expect that the number of residents who wait longer than the median waiting time will be
4) Considey molecules cnd 100 10 cells of equal energy. Find log. energy most probabile and ii the wfor j the distribution least probable distribution.
Suppose f(x) = 0.20 for 0 < x < 5. Determine the mean and variance of X. Mean = i (Round the answer to 2 decimal places.) Variance = i (Round the answer to 3 decimal places.)
Suppose that X and Y are unknowns with E(X) = 10, Var (X) = 4, E(Y)=12 and Var (Y) = 100. In addition, suppose that the correlation coefficient of X and Y is .6. Then what is the variance of X-Y?
5. Test whether the following expression is a valid pdf. If it is a valid pdf, obtain the CDF and its mean. 1 X 2x +) = -— exp( - ² ) + ²/12/² g(x)= X (+).x20 -exp
13
What is indicated by a Pearson correlation of r= +1.00 between X and Y? O Every increase in X causes an increase in Y Every change in X causes a change in Y O Each time X increases, there is a perfectly predictable increase in Y All of the other 3 choices occur with a correlation of +1.00.
Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.03. Suppose that on a given day 10 patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: None of these E(X)=0.5 and V(X)=0.475 E(X)=0.4 and V(X)=0.384 E(X)=0.3 and V(X)=0.291
Consider the model Y = B1 + B2X + e, which we estimate using a random sample with 12 observations. Let bj and b2 be the estimators for B1 and B2 and recall Eê, where ê; = Y; – bị – b2X;. Suppose the sample correlation between {X; }"_-1 and {Y;}"_, is 0.5 and E(Y; – Ỹ„)² = 100. What is ổ?? %3D n-2 Hint: (i) for simple regression, the regression R? is equal to the squared sample correlation between X and Y. (ii) R² = 1 – SSE where SSE = Eế and SST SST = O a. 7.5 O b. 8.5 О с. 9 O d. 10 O e. 8 O f. 7 Clear my choice
US STAST.

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6. Show that a gamma distribution with a > 1 has a relative maximum at x = (a- 1)ß. What happens when 0 < a < 1 and a = 1?