As a simplified model for weather forecasting, suppose that the weather (either wet or dry) tomorrow will be the same as the weather today with probability p. Show that the weather is dry on January 1, then Pn

, the probability that it will be dry n days layer, satisfies

Pn=(2p−1)Pn−1+(1−p)n≥1

P0=1

Prove that

Pn=1/2+1/2(2p−1)nn≥0

What is the multiplicative rate of change of the exponential function shown on the graph?

Segment xy is dilated through point m with a scale factor of 2. which segment shows the correct result of the dilation

17. a researcher measures three variables, x, y, and z for each individual in a sample of n = 20. the pearson correlations for this sample are rxy = 0.6, rxz = 0.4, and ryz = 0.7. a. find the partial correlation between x and y, holding z constant. b. find the partial correlation between x and z, holding y constant. (hint: simply switch the labels for the variables y and z to correspond with the labels in the equation.) gravetter, frederick j. statistics for the behavioral sciences (p. 526). cengage learning. kindle edition.