P4 Torch

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UltraFire 501B G60 6P CREE P4 LED Flashlight Torch Pressure Swtch Holster Set    US $22.55

UltraFire 1 mode on off WF 501B CREE P4 150 Lumens 18650 LED Flashlight Black    US $15.99

UltraFire WF 501B Tactical G60 6P CREE P4 LED Flashlight Torch Mount Set    US $23.85

UltraFire WF 501B CREE Red Green Blue Purple Light Bulb LED Flashlight Torch Kit    US $39.80

UltraFire C3 CREE P4 LED AA 14500 SS Flashlight Torch    US $9.89

UltraFire WF 501B 150LM CREE LED Red Light and Green Lihgt Bulb Flashlight Torch    US $23.25

UltraFire G60 Torch CREE LED Flashlight Red Light 6P hunter tactical defender    US $19.99

Ultrafire G60 Cree BLUE LED Flashlight Torch 6v 6p G2 E    US $19.18

UltraFire Blue CREE LED RCR123A 16340 Flashlight Torch Remote Pressure Switch 6p    US $22.88

Uwe CREE Red Light LED Flashlight hunter tactical defender hunting Torch 6P SIZE    US $33.88

Ultrafire W200 Diving Diver Scuba Cree LED AA X3 Flashlight Torch camping lamp    US $48.18

UltraFire 501B CREE LED Red Light Green Light Bulb Flashlight Torch RCR123A 501B    US $28.88

UltraFire WF 501B G60 6P CREE P4 LED Flashlight Tactical Pressure Swtch Set    US $22.45

UltraFire WF 501B 1Mode CREE LED Red Light and Green Lihgt Bulb Flashlight Torch    US $23.55

UltraFire C3 CREE P4 LED 14500 Flashlight Torch Charger    US $39.99

New 160LM F20 CREE P4 LED Hiking Flashlight Torch Aluminum Alloy AA    US $7.00

Ultrafire WF 501A Tactical CREE P4 LED Flashlight Torch Mount Remote Switch Set    US $19.55

Ultrafire G60 Cree RED LED Flashlight Torch 6v C8 501B P60 tactical hunting Lamp    US $16.68

3 72V 120L CREE P4 Replacement Bulb for Surefire Torch    US $9.99

Romisen RC 2B4 CREE P4 LED Flashlight 2 AAA Torch Lamp    US $19.99

3in1 Torch Flashlight 10 LED 5 UV Laser Pointer P4    US $6.99

TrustFire 1x16340 140Lumen CREE P4 LED Flashlight Torch    US $22.99

UltraFire C1 Tactical Body Holder Shell    US $16.99

New UltraFire WF 501B G60 Tactical Flashlight Torch Body For Q5 R2 T6 Xenon Bulb    US $7.98

X2000 Zooming Glass Optics Cree P4 WC LED Flashlight Torch Black New    US $.99

CREE Q5 WC LED 240 Lumen Zoomable Torch Flashlight Lamp    US $6.05

LED LENSER P4 TORCH Australian Warranty Hiking Camping Flashlight in Gift Box    US $37.98

Adjustable Focus Torch Zoom Flashlight CREE LED Batte    US $12.99

Spiderfire Infrared IR LED NVG Night Vision Flashlight    US $29.99

TERRALUX EXTREME LED BULB FOR C and D CELL MAGLITE FLASHLIGHT TORCH TLE 6EXB    US $14.95

Adjustable Focus CREE P4 200 Lumen LED AAA Flashlight    US $.99

Ultrafire WF 501A Tactical CREE P4 LED Flashlight Torch Remote Switch Mount Set    US $24.99

UltraFire 501B 1Mod CREE LED Red Light and Green Lihgt Bulb Flashlight Torch Set    US $38.99

RCG4 CREE P4 Q4 LED Torch Flashlight 18650 CHARGER    US $27.53

UltraFire WF 501B Tactical 18650 G60 6P CREE P4 LED Flashlight Torch Mount Set    US $27.72

UltraFire 501B 18650 Tactical CREE P4 LED Flashlight Torch Battery Mount Set    US $29.55

Romisen RC E4 P4 CREE LED CR123A Flashlight Torch 200LM    US $16.59

UltraFire Tactical 501B Flashlight 6P G60 Torch Body    US $10.89

200Lum CREE P4 Q4 LED Light Flashlight TorchHolster 8B    US $13.58

160 Lumens P4 CREE Led Flashlight Torch Lamp Holster    US $5.99

CREE Q5 WC LED 240 Lumens Torch Flash light Lamp 3AAA    US $6.15

Mini UltraFire C3 200LM Water Resistant CREE XR E P4 LED Flashlight Torch new    US $8.63

WF 602C Black 3w Cree P4 Pocket LED Mini 16340 Flashlight Torch 300LM 3 Mode    US $7.99

UltraFire WF 501B CREE P4 LED Flashlight Torch Lamp    US $10.34

UltraFire 501B Tactical CREE P4 LED Flashlight Torch Pressure Swtch Mount Set    US $19.55

Spiderfire L2 Xenon Tactical Flashlight Torch 6p G2 T    US $14.49

NEW 5W Zoom CREE Q3 LED Head waerproof FlashLight TORCH Headlamp Free Shipping    US $9.99

Spiderfire L2 Cree RED LED Flashlight Torch 6v 6p G2    US $23.99

Spiderfire L2 Xenon Tactical Flashlight Torch 6v 6p G2    US $14.49

CREE P4 200 LM LED Flashlight Torch Black    US $21.59

UltraFire WF 501B Cree P4 LED 1 mode Flashlight Torch Combo    US $20.50

WF 502B CREE P4 LED 18650 Flashlight Torch with Bike Clamp    US $16.50

UltraFire WF 501B Cree P4 LED 5 mode Flashlight torch with Holster    US $16.00

Black 3w Cree P4 3 Mode LED Mini Flashlight Torch 300LM    US $7.99

240Lum CREE Q5 WC Q4 LED Light Flashlight TorchHolster    US $6.15

Ultrafire L2 G60 Xenon Tactical Flashlight Torch 6v 6p    US $14.49

RCG4 CREE P4 Q4 LED Light Flashlight Torch BK Holster    US $17.12

BK Portable 300LM Cree P4 Pocket LED Mini Flashlight Torch 16340 Battery Charger    US $17.19

Mini P4 3 Mode LED Flashlight Torch 300LM 16340 Battery Charger Black 3in1    US $14.73

Silver mini P4 LED Flashlight Torch 300LM 16340 Battery Charger    US $14.73

Silver 3w Cree P4 3 Mode LED Mini Flashlight Torch 300L    US $9.33

New 160LM F20 CREE P4 LED Waterproof Flashlight Torch Aluminum Alloy AA    US $12.99

P4 CREE LED 200 Lumens Bulb f Superfire Surefire Torch    US $10.49

Trustfire TR 800 X5 CREE P4 5 Mode LED Flashlight Torch    US $54.99

Trustfire TR 800 X5 CREE P4 5 Mode LED Flashlight SET    US $77.99

Spiderfire L2 Cree GREEN LED Flashlight Torch 6v 6p G2    US $23.99

Spiderfire L2 Cree BLUE LED Flashlight Torch 6v 6p G2    US $23.99

Ultrafire C2 CREE P4 LED Rechargeable Flashlight Torch    US $48.99

Silver 3w Cree P4 Pocket LED Mini Flashlight Torch 80mm    US $7.99

UltraFire WF 501C CREE P4 LED Flashlight Torch Lamp    US $13.98

Silver 3w Cree P4 Pocket LED Mini Flashlight Torch 80mm Charger 16340 Battery    US $12.99

UltraFire WF 501B Cree P4 LED WF 139 Flashlight Torch 18650 battery Charger    US $29.00

Four 160 Lumens P4 CREE Led Flashlight Torch Lamp    US $11.18

UltraFire WF 502B CREE P4 LED Flashlight Torch Lamp    US $11.35

Cree P4 Tactical Camping Flashlight Torch w CR123A x2    US $26.05

Tactical Head Spiderfire Red P4 LED Flashlight w CR123A    US $28.04

Tactical Spiderfire Green P4 LED Flashlight w CR123A2    US $28.04

P4 Pressure On ON Switch Flashlight TorchMountCR123A    US $48.53

400LM zoomable CREE Q5 SA 28 LED flashlight Three modes with Dimmer USA new    US $9.98

UltraFire WF 501B Cree P4 LED 1 mode 18650 Flashlight Torch    US $15.50

random variable question(exponential distribution...find the probability)?

There are 30 students in a marathon race with their t-shirts numbered as P1, P2, P3, P4…P30. As soon as P1 gets tired, he/she hands over the torch to P2 and he/she starts running. When P2 stops, P3 starts running and so on. Assuming that the time for a player Pi to get tired is an exponentially distributed random variable with parameter Q= 0.1 (minutes)^-1.

The sum of independent and identically distributed Exponential random variables follow a Gamma distribution with parameters n, the number of Exponentials summed together, and Q, the same parameter from the Exponential distribution.

the pdf for T ~ Gamma( n, Q ) is:

f(t) = t^(n-1) exp( -t / Q ) / ( Γ(n) Q^n)

in this case we have n = 30 and Q = 0.1

Find P(T > 350) =

∞
∫ t^(29) exp( -t / 0.1 ) / ( Γ(30) 0.1^30) dt
350

Using R to get the numeric value instead of dealing with the horrible integral I get:

> pgamma(350, shape = 30, scale = 1/0.1, lower.tail = FALSE)
[1] 0.1770455

The probability the 30 runners will total time greater than 350 is 0.1770455

10000 * 0.1770455 = 1770.455