please help me i need it done fast ill give brainest !! its a e+am ( i can't put the real word bc brainly will delete it )

Mathematics

1 answer:

iris [78.8K]3 years ago

8 0

Answer:

Step-by-step explanation:

Continental Drift Theory says that all the continents used to be one landmass called Pangaea, and that proves how glaciers, fossils, and plants are on different sides of oceans.

(Is proven to be true.)

So that leaf must have came from a tropical landmass like Australia, Africa, or South America.

Since C is the one that explains Plate Tectonic Theory, it is correct.

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Let Xi,X2,X3,... be i.i.d. Bernoulli trials with success probability p and Sk=X1+.....+Xk. Let m< n.

Kay [80]

Answer:

Detailed step wise solution is given below:

Step-by-step explanation:

If X_i,i=1,2,3,... are Bernoulli random variables, then its PMF is

P\left (X_i =1 \right )=p, P\left (X_i =0 \right )=1-p,i=1,2,3,...

Define S_k=X_1+X_2+...+X_k . When S_n=k,0\leqslant k\leqslant n. Then k out of n random variables equals to 1. There are \binom{n}{k} possible combinations of k 1's and n-k 0's. So we have

P\left ( S_n=k \right )=\binom{n}{k}p^k\left ( 1-p \right )^{n-k},k=0,1,2,...,n . That is S_n has Binomial distribution.

a)The joint probability mass function of random vector \left ( X_1,X_2,...,X_m \right ) given S_n=X_1+X_2+...+X_n=k defined as \left (n\geqslant m \right )

P\left ( X_1=a_1,X_2=a_2,...,X_m=a_m|S_n=k \right ) can be calculated as below.

P\left ( S_m=l,S_n=k \right )=\binom{m}{l}p^l\left ( 1-p \right )^{m-l}\binom{n-m}{k-l}p^{k-l}\left ( 1-p \right )^{n-m-k+l}\\ P\left ( S_m=l,S_n=k \right )=\binom{m}{l}\binom{n-m}{k-l}p^k\left ( 1-p \right )^{n-k};l=0,1,2,..,m;k=l,..,n

The conditional distribution,

P\left ( S_m=l|S_n=k \right )=\frac{P\left ( S_m=l,S_n=k \right )}{P\left ( S_n=k \right )}\\ P\left ( S_m=l|S_n=k \right )=\frac{\binom{m}{l}\binom{n-m}{k-l}p^k\left ( 1-p \right )^{n-k}}{\binom{n}{k}p^k\left ( 1-p \right )^{n-k}}\\ {\color{Blue} P\left ( S_m=l|S_n=k \right )=\frac{\binom{m}{l}\binom{n-m}{k-l}}{\binom{n}{k}};l=0,1,2,..,m;k=l,..,n}

This distribution is Hyper geometric distribution. We have to get l successes in first m trials and k-l successes in the next n-m trials. The total ways of happening this is \binom{n}{k} . Hence Hyper geometric.

b) The conditional expectation is

E\left ( S_m=l|S_n=k \right )=\sum_{l=0}^{m}lP\left ( S_m=l|S_n=k \right )\\ E\left ( S_m=l|S_n=k \right )=\sum_{l=0}^{m}l\times \frac{\binom{m}{l}\binom{n-m}{k-l}}{\binom{n}{k}}\\

Use the formula for expectation of hyper geometric distribution, {\color{Blue} E\left ( S_m=l|S_n=k \right )=\frac{k m}{n}}

7 0

4 years ago

You own a company that employs three salespeople, Quentin, Michael and Bubba. Quentin makes 30% of the sales, Michael 45%, and B

borishaifa [10]

Answer:

Michael

Step-by-step explanation:

Look at the table below:

The probability of selecting a sale that was made by Quentin is .30, by Michael is .45 and by Bubba is .25.

Since Quentin completes paperwork 90% of the time, he doesn't complete paperwork 10% of the time, following this reasoning we can say that Michael doesn't complete paperwork 20% of the time and Bubba doesn't complete paperwork 15% of the time.

The probability of selecting a file and that it belongs to Quentin AND is incomplete is:

(Probability of selecting a Quentin's file) x (Probability is a Quentin incomplete file) = (0.30)(0.10) = 0.03

Using this same method we have that the probability that it belongs to Michael and is incomplete is (.45)(.20) = 0.09

That it belongs to Bubba and it's incomplete is (0.25)(0.15) = 0.037

The highest of these probabilities is the one that corresponds to Michael: 0.09, therefore he is the most likely culprit.