Question

mal dis ca 7) A spinner has the following probability distribution: AC boasin oy wPt. Value Probability .1 30 7 60 2 a) Explain how we know this is a valid probability distribution: b) What is its expected value? Give the formula, substitution and result. iS uld ( c) What is its population variance? Give the formula, substitution and result. Sealchem ould o ( d) What is the population standard deviation?

Answer 1

solution : Given that pt value (xi) probability (Pi) 300 60 .7. 02 as conditions for a i Pi »oitti cie pi Epi al probability all pi are distribution positive) Here & all Epi Pixo : 0.1 +0.7 +0.2 distribution is a vould probablity ₃. Given probability distribution - by = E(X) find expected value Formula EX) = & xipi E = Ox01 + 30 x07 + 60 x0.2 E = ot 21 + 12 EX 33 e expected value is 33 cy population variance = r2 . find formala 6 = E(X) - EC)

where E(X²) = { xi²pi = 0²xo 1 + 30²x0.7+ 60²x0.2 = 0+ goox0.7 + 3000 xo. 2 = 636 +720 E (X²) = 1350 and Elx) = 33 find in part by - popiutation variance = r² = E(X²) - E(X) ² = 1850 -83) = 1350 - 1089 5 - 26 poplulation variance is 261... dy population standard deviation or 8= vuaniance = √261 - find in part at o = 16 ISSS population standard deviation is 16.1555 .