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rusak2 [61]
4 years ago
15

Could someone explain linear functions to me? I dont get them at all. Thanks!

Mathematics
1 answer:
BigorU [14]4 years ago
3 0

Answer:

Step-by-step explanation:

Linear functions are whose graph is a straight line. They contain a slope and a constant also known as the y intercept.

Example: y = 3x + 2

The slope is 3 and the y intercept is 2.

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A municipal bond service has three rating categories (A, B, and C). Suppose that in the past year, of the municipal bonds issued
11Alexandr11 [23.1K]

Answer:

(a) The probability that the new municipal bond issued will receive an A rating given that it was issued by a city is 0.196.

(b) Thus, the probability of municipal bonds issued by suburbs is 0.325.

Step-by-step explanation:

The data provided is as follows:

P (A) = 0.70

P (B) = 0.20

P (C) = 0.10

P (c | A) = 0.50

P (s | A) = 0.40

P (r | A) = 0.10

P (c | B) = 0.60

P (s | B) = 0.20

P (r | B) = 0.20

P (c | C) = 0.90

P (s | C) = 0.05

P (r | C) = 0.05

(a)

The Bayes' theorem states that the conditional probability of an event <em>Y</em>_{i} given that another event <em>X</em> has already occurred is:

P(Y|X)=\frac{P(X|Y)P(Y)}{\sum\limits_{i} {P(X|Y_{i})P(Y_{i})}}

Compute the probability that the new municipal bond issued will receive an A rating given that it was issued by a city as follows:

P(A|c)=\frac{P(c|A)P(A)}{P(c|A)P(A)+P(c|B)P(B)+P(c|C)P(C)}

           =\frac{(0.50\times 0.70)}{(0.50\times 0.70)+(0.60\times 0.20)+(0.10\times 0.90)}\\\\=\frac{0.35}{0.56}\\\\=0.196

Thus, the probability that the new municipal bond issued will receive an A rating given that it was issued by a city is 0.196.

(b)

The law of total probability states that:

P(X)=\sum\limits_{i} {P(X|Y_{i})}

Compute the probability of municipal bonds issued by suburbs as follows:

P(s)=P(s|A)P(A)+P(s|B)P(B)+P(s|C)P(C)

        =(0.40\times 0.70)+(0.20\times 0.20)+(0.10\times 0.05)\\\\=0.28+0.04+0.005\\\\=0.325

Thus, the probability of municipal bonds issued by suburbs is 0.325.

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Answer:
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