My thread of questions

[khalil]

Please help

If Z has the standard normal distribution and Pr(Z< c)= a, where 0<c<3 and 0<a<1, then Pr(|Z|<c) is equal to:

ans. 2a-1

[TrueTears]

Pr(|Z| < c) is the same as Pr(-c < Z < c)

so since Pr(Z < c) = a

then Pr(Z > c) = 1-a

Using symmetry Pr(Z < -c) = 1-a

Therefore the area between -c and c is 1-(2(1-a)) = 1 - 2 + 2a = 2a - 1.

[khalil]

thanks bro

[khalil]

What does the are under a graph represent?

[TrueTears]

What does the are under a graph represent?

?

[NE2000]

What does the are under a graph represent?

Under a pdf (including a normal distribution curve), it represents the probability

If that's not what you're asking, I empathize with TT

[khalil]

My sincere apologies, I mean in terms of integration, I've found the area under the graph so much, but what does it represent. Like, can you give me an example of a situation in which it is used.

[Flaming_Arrow]

when you integrate a function, ur pretty much multiplying  y* x, eg. under a velocity-time graph, its the displacement which is just velocity * time

[khalil]

What does proportional mean in terms of maths, eg. the nubmber of new days is proportional  to p(t). Does that simply mean there is a difference between both is a constant?

[zzdfa]

it means new days = k * p(t) for some constant k

[khalil]

so does that mean proportion of one thing and another is the multiple of k?

[Flaming_Arrow]

so does that mean proportion of one thing and another is the multiple of k?

it means when one thing increases, other thing increases too

[khalil]

At each of a series of trials, the probability of the occurence of a certain event is 0.5, except this cannot occur in 2 consecutive trials.

Show that the prob. of it occuring just twice in three trials is 0.25.
ans.
E=event
N=no event

ENE= 0.5*1*0.5= 0.25

My Question: why is N, 1?

[shinny]

At each of a series of trials, the probability of the occurence of a certain event is 0.5, except this cannot occur in 2 consecutive trials.

Show that the prob. of it occuring just twice in three trials is 0.25.
ans.
E=event
N=no event

ENE= 0.5*1*0.5= 0.25

My Question: why is N, 1?

Because it's stated that the event (E) cannot occur in 2 consecutive trials. If E cannot occur, then N must occur, therefore Pr(N)=1.

[khalil]

I don't understand. I thought if E cannot occur then N would be 1-0.5