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3 years ago

Solve for x. x2 - 49 = 0 A) 0 B) ±49 C) ±49i D) ±7

Mathematics

2 answers:

Nikolay [14]3 years ago

6 0

Answer:

Step-by-step explanation:

x^2=49 -> 7

x^2=-49 -> -7

really need brainliest - it would be appreciated

xxTIMURxx [149]3 years ago

3 0

The correct answer is D.

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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 answer is 4,6,7

gtnhenbr [62]

Answer:

Nice for you

Step-by-step explanation:

Nice for you

5 0

3 years ago

Layla and Bobby want to make 10 potholders each. If it takes one-eighth of a yard to make each potholder, how much total fabric

Yuki888 [10]

Answer: 1.25
explanation: you multiply the amount of fabric used for one by the amount of potholders
.125 x 10 = 1.25

4 0

3 years ago

2/8 + 6/12 what is that eqaul to

Papessa [141]

$\frac{2}{8} + \frac{6}{12} \\ \\ \frac{1}{4} + \frac{1}{2} \\ \\ LCD = 4 \\ \\ \frac{1}{4} + \frac{2}{4} \\ \\ \frac{1+2}{4} \\ \\ \frac{3}{4} \\ \\ Answer: \fbox {3/4} \ or \ \fbox {0.75}$

8 0

3 years ago

Read 2 more answers

at the snack shack, students attending the football game can buy sodas for $1 and slices of pizza for $3. At fridays game, the s

hram777 [196]

Answer:

126-pizza

124- soda

Step-by-step explanation:

4 0

3 years ago