Find the slope y=3x+7
2 answers:
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![\bf \textit{Periodic Exponential Growth}\\\\ A=I(1 + r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &4100\\ r=rate\to 100\%\to \frac{100}{100}\to &1.00\\ t=\textit{elapsed time}\to &8\\ p=period\to &10 \end{cases} \\\\\\ A=4100(1 + 1)^{\frac{8}{10}}\implies A=4100(2)^{\frac{4}{5}}\implies A=4100\sqrt[5]{2^4}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7BPeriodic%20Exponential%20Growth%7D%5C%5C%5C%5C%0AA%3DI%281%20%2B%20r%29%5E%7B%5Cfrac%7Bt%7D%7Bp%7D%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0AA%3D%5Ctextit%7Baccumulated%20amount%7D%5C%5C%0AI%3D%5Ctextit%7Binitial%20amount%7D%5Cto%20%264100%5C%5C%0Ar%3Drate%5Cto%20100%5C%25%5Cto%20%5Cfrac%7B100%7D%7B100%7D%5Cto%20%261.00%5C%5C%0At%3D%5Ctextit%7Belapsed%20time%7D%5Cto%20%268%5C%5C%0Ap%3Dperiod%5Cto%20%2610%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D4100%281%20%2B%201%29%5E%7B%5Cfrac%7B8%7D%7B10%7D%7D%5Cimplies%20A%3D4100%282%29%5E%7B%5Cfrac%7B4%7D%7B5%7D%7D%5Cimplies%20A%3D4100%5Csqrt%5B5%5D%7B2%5E4%7D)
Answer:
(a) The joint PMF of W, L and T is:
(b) The marginal PMF of W is:
Step-by-step explanation:
Let <em>X</em> = number of soccer games played.
The outcome of the random variable <em>X</em> are:
<em>W</em> = if a game won
<em>L</em> = if a game is lost
<em>T</em> = if there is a tie
The probability of winning a game is, P (<em>W</em>) = 0.60.
The probability of losing a game is, P (<em>L</em>) = 0.30.
The probability of a tie is, P (<em>T</em>) = 0.10.
The sum of the probabilities of the outcomes of <em>X</em> are:
P (W) + P (L) + P (T) = 0.60 + 0.30 + 0.10 = 1.00
Thus, the distribution of W, L and T is a appropriate probability distribution.
(a)
Now, the outcomes W, L and T are one experiment.
The distribution of <em>n</em> independent and repeated trials, each having a discrete number of outcomes, each outcome occurring with a distinct constant probability is known as a Multinomial distribution.
The outcomes of <em>X</em> follows a Multinomial distribution.
The joint probability mass function of <em>W</em>, <em>L</em> and <em>T</em> is:
The soccer tournament consists of <em>n</em> = 5 games.
Then the joint PMF of W, L and T is:
(b)
The random variable <em>W</em> is defined as the number games won in the soccer tournament.
The probability of winning a game is, P (W) = <em>p</em> = 0.60.
Total number of games in the tournament is, <em>n</em> = 5.
A game is won independently of the others.
The random variable <em>W</em> follows a Binomial distribution.
The probability mass function of <em>W</em> is:
Thus, the marginal PMF of W is: