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Alex17521 [72]
4 years ago
9

If 3 suspects who committed a burglary and 6 innocent persons are lined up, what is the probability that a witness who is not su

re and has to pick three persons will pick the three suspects by chance? That the witness picks 3 innocent persons by chance?
Mathematics
1 answer:
Nataly [62]4 years ago
7 0
The number of ways you can pick 3 people from 9 = 9*8*7 / 3*2*1 = 84

So chance of picking the 3 suspects = 1 / 84.

The number of ways to pick 3 from the 6 innocent people = 6*5*4 / 3*2*1 = 20

Chances of picking 3 innocent people = 20 / 84  or 5/21

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4 years ago
Graph the linear inequality.<br> y&lt;2
Leya [2.2K]

Answer:

See attachment.

Step-by-step explanation:

We want to graph the linear inequality y<2

We  first of all graph  the corresponding linear equation y=2 with a dashed line because all points on this line do not satisfy the inequality.

We then shade below the line y=2, to show that all points below the boundary line are solution to the inequality y<2

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3 years ago
Two surveys were independently conducted to estimate a population mean, μ. denote the estimates and their standard errors by x1
lyudmila [28]

Hi there what you need is lagrange multipliers for constrained minimisation. It works like this,

V(X)=α2σ2X¯1+β2\sigma2X¯2

Now we want to minimise this subject to α+β=1 or α−β−1=0.

We proceed by writing a function of alpha and beta (the paramters you want to change to minimse the variance of X, but we also introduce another parameter that multiplies the sum to zero constraint. Thus we want to minimise

f(α,β,λ)=α2σ2X¯1+β2σ2X¯2+λ(\alpha−β−1).

We partially differentiate this function w.r.t each parameter and set each partial derivative equal to zero. This gives;

∂f∂α=2ασ2X¯1+λ=0

∂f∂β=2βσ2X¯2+λ=0

∂f∂λ=α+β−1=0

Setting the first two partial derivatives equal we get

α=βσ2X¯2σ2X¯1

Substituting 1−α into this expression for beta and re-arranging for alpha gives the result for alpha. Repeating the same steps but isolating beta gives the beta result.

Lagrange multipliers and constrained minimisation crop up often in stats problems. I hope this helps!And gosh that was a lot to type!xd

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Kaylis [27]
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How do you use estimation to help find the product of 2 decimals??
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