Zadanie 1c
Now let w=4 and p=1/3. Express R₂ in terms of R₁ and R₃.
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Now let w=4 and p=1/3. Express R₂ in terms of R₁ and R₃.
For w=4 and p=1/3 it is known that R₁=1/15 and R₃=7/15. Find R₂.
For general 0<p<1 with p≠q, replace Rₙ by (p+q)Rₙ in the recurrence and prove Rn+1 − Rn = (q/p)(Rn − Rn−1).
(i) Use R₀=0 to express R₂−R₁ in terms of p,q,R₁. (ii) Show that R3 − R2 = (q/p)2R1. (iii) Deduce the general expression for Rₙ−Rₙ₋₁.
(i) By adding successive differences, or otherwise, prove . (ii) Given R1 = [1 − q/p]/[1 − (q/p)w], deduce Rn = [1 − (q/p)n]/[1 − (q/p)w].
The upward-tick probability is now 0.498. A run starts with m charge units and stops successfully when it has accumulated 12 additional units, so capacity is w=m+12. Find the smallest positive integer m giving at least an 85% chance of success.
How many sampled workers belong to department D?
The diagram summarizes the sample. State the median.
The interquartile range is 14 minutes. Find a.
An outlier is below Q₁−1.5IQR or above Q₃+1.5IQR. Find the smallest commuting time permitted by this rule without being a lower outlier.