Which of the following are perfect squares? Check all that apply.

For X a binomial random variable with n=5 and p=1/4, answer the following

mash [69]

Recall that for $X\sim\mathrm{Bin}(n,p)$ , i.e. a random variable $X$ following a binomial distribution over $n$ trials and with probability parameter $p$ ,

$\mathbb P(X=x)=f_X(x)=\begin{cases}\dbinom nx p^x(1-p)^{n-x}&\text{for }x\in\{0,1,\ldots,n\}\\\\0&\text{otherwise}\end{cases}$

So you have

$\mathbb P(X=2)=\dbinom52\left(\dfrac14\right)^2\left(1-\dfrac34\right)^{5-2}=\dfrac{135}{512}\approx0.26$

$\mathbb P(2\le X\le4)=\displaystyle\sum_{x=2}^4\mathbb P(X=x)$
$=\dbinom52\left(\dfrac14\right)^2\left(1-\dfrac14\right)^{5-2}+\dbinom52\left(\dfrac14\right)^3\left(1-\dfrac14\right)^{5-3}+\dbinom52\left(\dfrac14\right)^4\left(1-\dfrac14\right)^{5-4}$
$=\dfrac{375}{1024}\approx0.37$

The expected value of $X\sim\mathrm{Bin}(n,p)$ is simply $np$ , while the standard deviation is $\sqrt{np(1-p)}$ . In this case, they are $\dfrac54=1.25$ and $\sqrt{\dfrac{15}{16}}\approx0.97$ , respectively.

7 0

3 years ago

1. Gala Farms sells a 3.5 pound bag of apples

ASHA 777 [7]

The cost per pound for the Gala farms is $1.20 per pound and For the Golden Orchard its $1.05 per pound. Which the Golden Orchard is better since its cheaper and costs 15 cents less.

7 0

2 years ago

The first step in factoring a trinomial of the form is to find two numbers, m and n, such that m + n = b and _____.

Licemer1 [7]

Answer:

Correct choice is C). mn=ac

Step-by-step explanation:

Given statement is that the first step in factoring a trinomial of the form is to find two numbers, m and n, such that m + n = b and _____.

We know that when we factor polynomial of type $ax^2+bx+c$ ,product of both numbers m and n must be same as product of a and c.