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seraphim [82]
3 years ago
8

This is probably pretty easy, I could solve all the other ones but I got stuck on this one.

Mathematics
1 answer:
anyanavicka [17]3 years ago
8 0

Answer:

78

Step-by-step explanation:

Let x be the score on the next test

We are averaging 6 tests and want an average of 75

( 82+91+38+78+83+x) /6 = 75

Multiply each side by 6

( 82+91+38+78+83+x) = 75*6

( 82+91+38+78+83+x)  =450

Combine like terms

x+372 = 450

Subtract 372 from each side

x+372-372 = 450-372

x =78

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5.2.14. For the negative binomial pdf p (k; p, r) = k+r−1 (1 − p)kpr, find the maximum likelihood k estimator for p if r is know
Volgvan

Answer:

\hat p = \frac{r}{\bar x +r}

Step-by-step explanation:

A negative binomial random variable "is the number X of repeated trials to produce r successes in a negative binomial experiment. The probability distribution of a negative binomial random variable is called a negative binomial distribution, this distribution is known as the Pascal distribution".

And the probability mass function is given by:

P(X=x) = (x+r-1 C k)p^r (1-p)^{x}

Where r represent the number successes after the k failures and p is the probability of a success on any given trial.

Solution to the problem

For this case the likehoof function is given by:

L(\theta , x_i) = \prod_{i=1}^n f(\theta ,x_i)

If we replace the mass function we got:

L(p, x_i) = \prod_{i=1}^n (x_i +r-1 C k) p^r (1-p)^{x_i}

When we take the derivate of the likehood function we got:

l(p,x_i) = \sum_{i=1}^n [log (x_i +r-1 C k) + r log(p) + x_i log(1-p)]

And in order to estimate the likehood estimator for p we need to take the derivate from the last expression and we got:

\frac{dl(p,x_i)}{dp} = \sum_{i=1}^n \frac{r}{p} -\frac{x_i}{1-p}

And we can separete the sum and we got:

\frac{dl(p,x_i)}{dp} = \sum_{i=1}^n \frac{r}{p} -\sum_{i=1}^n \frac{x_i}{1-p}

Now we need to find the critical point setting equal to zero this derivate and we got:

\frac{dl(p,x_i)}{dp} = \sum_{i=1}^n \frac{r}{p} -\sum_{i=1}^n \frac{x_i}{1-p}=0

\sum_{i=1}^n \frac{r}{p} =\sum_{i=1}^n \frac{x_i}{1-p}

For the left and right part of the expression we just have this using the properties for a sum and taking in count that p is a fixed value:

\frac{nr}{p}= \frac{\sum_{i=1}^n x_i}{1-p}

Now we need to solve the value of \hat p from the last equation like this:

nr(1-p) = p \sum_{i=1}^n x_i

nr -nrp =p \sum_{i=1}^n x_i

p \sum_{i=1}^n x_i +nrp = nr

p[\sum_{i=1}^n x_i +nr]= nr

And if we solve for \hat p we got:

\hat p = \frac{nr}{\sum_{i=1}^n x_i +nr}

And if we divide numerator and denominator by n we got:

\hat p = \frac{r}{\bar x +r}

Since \bar x = \frac{\sum_{i=1}^n x_i}{n}

4 0
3 years ago
The inequality of the graph
fiasKO [112]

Answer:

\displaystyle y > 4x - 2

Step-by-step explanation:

Starting from the y-intercept of \displaystyle [0, -2],you do \displaystyle \frac{rise}{run}by either moving four blocks <em>south</em><em> </em>over one block <em>west</em><em> </em>or four blocks <em>north</em><em> </em>over one block<em> east</em><em> </em>[<em>west</em> and <em>south</em> are negatives]. Next, we have to determine the types of inequality symbols that are suitable for this graph, which will be <em>less</em><em> </em><em>than</em><em> </em>and <em>greater</em><em> </em><em>than</em><em> </em>since this is a <em>dashed</em><em> </em><em>line</em><em> </em>graph. We then use the zero-interval test [test point (0, 0)] to ensure whether we shade the opposite portion [portion that does not contain the origin] or the portion that DOES contain the origin. At this step, we must verify the inequalities as false or true:

<em>Greater</em><em> </em><em>than</em>

\displaystyle 0 > 4[0] - 2 → 0 > -2☑

<em>Less</em><em> </em><em>than</em><em> </em>

\displaystyle 0 < 4[0] - 2 → 0 ≮ -2

This graph is shaded in the portion of the origin, so you would choose the <em>greater</em><em> </em><em>than</em><em> </em>inequality symbol to get this inequality:

\displaystyle y > 4x - 2

I am joyous to assist you anytime.

3 0
3 years ago
5x3 + 14x2 + 9x <br> help
Cerrena [4.2K]
<h3>Answer:    x(x+1)(5x+9) </h3>

===================================================

Work Shown:

5x^3 + 14x^2 + 9x

x( 5x^2 + 14x + 9 )

To factor 5x^2 + 14x + 9, we could use the AC method and guess and check our way to getting the correct result.

A better way in my opinion is to solve 5x^2 + 14x + 9 = 0 through the quadratic formula

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(14)\pm\sqrt{(14)^2-4(5)(9)}}{2(5)}\\\\x = \frac{-14\pm\sqrt{16}}{10}\\\\x = \frac{-14\pm4}{10}\\\\x = \frac{-14+4}{10} \ \text{ or } \ x = \frac{-14-4}{10}\\\\x = \frac{-10}{10} \ \text{ or } \ x = \frac{-18}{10}\\\\x = -1 \ \text{ or } \ x = \frac{-9}{5}\\\\

Then use those two solutions to find the factorization

x = -1  or  x = -9/5

x+1 = 0  or  5x = -9

x+1 = 0  or  5x+9 = 0

(x+1)(5x+9) = 0

So we have shown that 5x^2 + 14x + 9 factors to (x+1)(5x+9)

-----------

Overall,

5x^3 + 14x^2 + 9x

factors to

x(x+1)(5x+9)

6 0
3 years ago
Please help. will mark brainliest
Otrada [13]

Answer: AC = A'C'

Then you can use the hypotenuse leg theorem to say that the two triangles are similar

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
There is a bag filled with 4 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it i
Orlov [11]

Answer:

Its a good probability

Step-by-step explanation:

7 0
3 years ago
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