Suppose the probability that you get an A in any class you take is .3 and the probability that you get a B is .7. To construct a grade point average, an A is worth 4.0 and a B is worth 3.0. a. What is the expected value for your grade point average? b. Would you expect to have this grade point average for each quarter or semester of your school career? Explain.

a) E(X) = 3.30

b) If these are the only two grades (A and B) available in the school, then this calculated expected value will truly be the expected GPA for each quarter or semester But, if like real life, there are other grades available at the school not included in this calculation, then this value seizes to be the expected value for the GPA over any time period.

Step-by-step explanation:

P(X=xᵢ) = pᵢ

For an A,

P(X=4.0) = 0.3

For a B

P(X=3.0) = 0.7

But E(X) = Σ xᵢpᵢ

E(X) = (0.3 × 4.0) + (0.7 × 3.0) = 3.30

b) If these are the only two grades available in the school, then this calculated expected value will truly be the expected GPA for each quarter or semester But, if like real life, there are other grades available at the school not included in this calculation, then this value seizes to be the expected value for the GPA over any time period.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

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step-by-step explanation: