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3 years ago

Can you please help me I’m not a 100% sure how to do this

Mathematics

2 answers:

DedPeter [7]3 years ago

8 0

Answer:

1/400

Step-by-step explanation:

Decimals are the number over how every many places the number is.

The number shown is 25. It goes out to the ten thousandths place. This means that you have to place 25 over 10,000 and simplify the fraction.

25/10,000 = 1/400

kolbaska11 [484]3 years ago

3 0

Answer:

1/400

Step-by-step explanation:

0025/100000=25/100000=5/2000=1/400

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What is the probability that all the roots of x2 + bx + c = 0 are real? [0,1]?

notsponge [240]

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$b^2-4c\ge0\implies b^2\ge4c$

Your question about probability is currently impossible to answer without knowing exactly what the experiment is. Are you picking $b,c$ at random from some interval? Is the choice of either distributed a certain way?

I'll assume the inclusion of "[0,1]" in your question is a suggestion that both $b,c$ are chosen indepently of one another from [0, 1]. Let $B,C$ denote the random variables that take on the values of $b,c$ , respectively. I'll assume $B,C$ are identical and follow the standard uniform distribution, i.e. they each have the same PDF and CDF as below:

$f_X(x)=\begin{cases}1&\text{for }0$

$F_X(x)=\begin{cases}0&\text{for }x$

where $X$ is either of $B,C$ .

Then the question is to find $P(B^2\ge4C)$ . We have

$P(B^2\ge4C)=P\left(C\le\dfrac{B^2}4\right)$

and we can condition the random variable $C$ on the event of $B=b$ by supposing

$P\left(C\le\dfrac{B^2}4\right)=P\left(\left(C\le\dfrac{B^2}4\right)\land(B=b)\right)=P\left(C\le\dfrac{B^2}4\mid B=b\right)\cdot P(B=b)$

then integrate over all possible values of $b$ .

$=\displaystyle\int_{-\infty}^\infty P\left(C\le\dfrac{b^2}4\right)f_B(b)\,\mathrm db$

$=\displaystyle\int_{-\infty}^\infty F_C\left(\dfrac{b^2}4\right)f_B(b)\,\mathrm db$

$=\displaystyle\int_0^1\dfrac{b^2}4\,\mathrm db=\frac1{12}$

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3 years ago

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