Two newspapers compete for subscriptions in a region with 300,000 households. Assume that no household subscribes to both newspapers and that the following table gives the probabilities that a household will change its subscription status during the year. From A From B From None To A .70 .15 .30 To B .20 .80 .20 To None .10 .05 .50 For example, an interpretation of the first column of the table is that during a given year, newspaper A can expect to keep 70 % of its current subscribers while losing 20 % to newspaper B and 10 % to no subscription. At the beginning of aparticular year, suppose that 150,000 househol;ds subscribe to newspaper A, 100,000 households subscribe to newspaper B, and 50,000 have no subscription.Let P and x be defined by P = 0.70 0.15 0.30 0.20 0.80 0.20 0.10 0.05 0.50 x = 150,000 100,000 50,000 The vector x is called state vector for the beginning of the year. Calculate P x and P 2 x and interpret the resulting vectors .
Two newspapers compete for subscriptions in a region with 300,000 households. Assume that no household subscribes to both newspapers and that the following table gives the probabilities that a household will change its subscription status during the year. From A From B From None To A .70 .15 .30 To B .20 .80 .20 To None .10 .05 .50 For example, an interpretation of the first column of the table is that during a given year, newspaper A can expect to keep 70 % of its current subscribers while losing 20 % to newspaper B and 10 % to no subscription. At the beginning of aparticular year, suppose that 150,000 househol;ds subscribe to newspaper A, 100,000 households subscribe to newspaper B, and 50,000 have no subscription.Let P and x be defined by P = 0.70 0.15 0.30 0.20 0.80 0.20 0.10 0.05 0.50 x = 150,000 100,000 50,000 The vector x is called state vector for the beginning of the year. Calculate P x and P 2 x and interpret the resulting vectors .
Solution Summary: The author explains how to calculate the value of Pmathrmx and P2
Two newspapers compete for subscriptions in a region with
300,000
households. Assume that no household subscribes to both newspapers and that the following table gives the probabilities that a household will change its subscription status during the year.
From A
From B
From None
To A
.70
.15
.30
To B
.20
.80
.20
To None
.10
.05
.50
For example, an interpretation of the first column of the table is that during a given year, newspaper A can expect to keep
70
%
of its current subscribers while losing
20
%
to newspaper B and
10
%
to no subscription.
At the beginning of aparticular year, suppose that
150,000
househol;ds subscribe to newspaper A,
100,000
households subscribe to newspaper B, and
50,000
have no subscription.Let
P
and
x
be defined by
P
=
0.70
0.15
0.30
0.20
0.80
0.20
0.10
0.05
0.50
x
=
150,000
100,000
50,000
The vector
x
is called state vectorfor the beginning of the year. Calculate
P
x
and
P
2
x
and interpret the resulting vectors.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License