normal distribution | Revision Server | Page 1

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tough idol can someone help with part ii) please?

yo so

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do you know how to like

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transform normal random variables

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like what happens if you add or multiply normal varaibles

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ok so with normal random variables

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you know what the 2 numbers mean in the brackets

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the N(a, b) the a and b

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@tough idol

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awesome so if you imagine

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lets just say for example its N(5, 36) just to give numbers

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if you imagine subtracting 3 off this random variable

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do you see how thatll be the same as just

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a normal but with a mean thats 3 lower

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aka N(2, 36)

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and if you instead multiply by a number

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say multiply by 2

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thatll be the same as a new normal but with a mean thats twice as big, but also a standard deviation thats twice as big

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because everything doubles, so the average distance apart also doubles

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close

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36 is the standard deviation squared

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actually yeah i said that wrong earlier

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its the s.d. squared so 36 means s.d. is 6

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so your new normal will be N(10, 144) instead

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yep

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make sense?

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awesome so

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with your question we have N(u, u^2/9)

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and want P(N(u, u^2/9) > 1.5u)

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now can we use some of the ideas about

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adding and multiplying (or subtracitng and dividing)

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to turn this N(u, u^2/9) into a nicer one

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maybe one without u

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yep sure

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yeah so whats your reasoning for that

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yep cool

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note that you can multiply by 3 instead

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(remmeber its squared for the 2nd number)

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so what would the new normal be

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if you multiplied it by 3

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u^2 for the 2nd but yep

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dw its cool

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but yep ok

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how about getting rid of the u it looks kinda annoying

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what could we do for that

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either

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well preferably both

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theyre both a problem

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awesome yeah

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so what would the new normal be now

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perfect

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now im gonna keep us with that because

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N(3, 1) we can actually kinda work with right

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its just numbers

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now if we look at out

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P(Y > 1.5u)

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well what did we do to Y to simplify it

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yep and also

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yep so

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if we turn Y to N(3,1)

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we should really do the same to the other side of the inequality right

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awesome

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so what will the 1.5u become

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awesome so now the question is

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P( N(3, 1) > 4.5)

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which is kinda the same question as your first question

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yep!

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no worries at all 😄

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now you just gotta remmeber it!

#normal distribution