You want to calculate the probability that a normally distributed variable with mean 0 and variance 1 lies between -1 and 1 using erf. Which formula correctly computes this probability?

hard📝 Application Q15 of 15

SciPy - Constants and Special Functions

You want to calculate the probability that a normally distributed variable with mean 0 and variance 1 lies between -1 and 1 using erf. Which formula correctly computes this probability?

A0.5 * (erf(1) + erf(-1))

Berf(1) - erf(-1)

C0.5 * (erf(1 / sqrt(2)) - erf(-1 / sqrt(2)))

Derf(1 / 2) - erf(-1 / 2)

Step-by-Step Solution

Solution:

Step 1: Recall normal distribution probability formula using erf
Probability between a and b for standard normal is 0.5*(erf(b/sqrt(2)) - erf(a/sqrt(2))).
Step 2: Apply formula for a=-1, b=1
Plugging in gives 0.5*(erf(1/sqrt(2)) - erf(-1/sqrt(2))).
Final Answer:
0.5 * (erf(1 / sqrt(2)) - erf(-1 / sqrt(2))) -> Option C
Quick Check:
Use erf(x/sqrt(2)) formula = A [OK]

Quick Trick: Divide limits by sqrt(2) before erf, multiply difference by 0.5 [OK]

Common Mistakes:

MISTAKES

Using erf directly without dividing by sqrt(2)
Adding erf values instead of subtracting
Ignoring the 0.5 multiplier

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You want to calculate the probability that a normally distributed variable with mean 0 and variance 1 lies between -1 and 1 using erf. Which formula correctly computes this probability?

Step 1: Recall normal distribution probability formula using erf

Step 2: Apply formula for a=-1, b=1

Final Answer:

Quick Check:

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